{"id":4344,"date":"2023-12-18T09:38:39","date_gmt":"2023-12-18T04:08:39","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=4344"},"modified":"2023-12-19T17:49:15","modified_gmt":"2023-12-19T12:19:15","slug":"samacheer-kalvi-12th-maths-solutions-chapter-3-ex-3-7","status":"publish","type":"post","link":"https:\/\/samacheerkalviguru.com\/samacheer-kalvi-12th-maths-solutions-chapter-3-ex-3-7\/","title":{"rendered":"Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 3.7"},"content":{"rendered":"

You can Download Samacheer Kalvi 12th Maths Book Solutions<\/a> Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.<\/p>\n

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 3.7<\/h2>\n

Choose the correct or the most suitable answer from the given four alternatives:<\/p>\n

Question 1.
\nA zero of x3<\/sup> + 64 is _______
\n(a) 0
\n(b) 4
\n(c) 4i
\n(d) -4
\nAnswer:
\n(d) -4
\nHint: x3<\/sup> + 64 = 0
\n\u21d2 x3<\/sup> = -64
\n\u21d2 x3<\/sup> = (-4)3<\/sup>
\n\u21d2 x = -4<\/p>\n

Question 2.
\nIf f and g are polynomials of degrees m and n respectively, and if h(x) = (f 0 g) (x), then the degree of h is ______
\n(a) mn
\n(b) m + n
\n(c) mn<\/sup>
\n(d) nm<\/sup>
\nAnswer:
\n(a) mn<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nA polynomial equation in x of degree n always has _______
\n(a) n distinct roots
\n(b) n real roots
\n(c) n imaginary roots
\n(d) at most one root.
\nAnswer:
\n(c) n imaginary roots (Every real number is also imaginary)<\/p>\n

Question 4.
\nIf \u03b1, \u03b2 and \u03b3 are the zeros of x3<\/sup> + px2<\/sup> + qx + r, then \\(\\sum \\frac{1}{\\alpha}\\) is ______
\n(a) \\(-\\frac{q}{r}\\)
\n(b) \\(\\frac{q}{p}\\)
\n(c) \\(\\frac{q}{r}\\)
\n(d) \\(-\\frac{q}{p}\\)
\nAnswer:
\n(a) \\(-\\frac{q}{r}\\)
\nHint:
\n\"Samacheer<\/p>\n

Question 5.
\nAccording to the rational root theorem, which number is not possible rational zero of 4x7<\/sup> + 2x4<\/sup> – 10x3<\/sup> – 5?
\n(a) -1
\n(b) \\(\\frac{5}{4}\\)
\n(c) \\(\\frac{4}{5}\\)
\n(d) 5
\nAnswer:
\n(c) \\(\\frac{4}{5}\\)
\nHint:
\nan<\/sub> = 4; a0<\/sub> = 5
\nLet \\(\\frac{p}{q}\\) be the root of P (x). P must divide 5, possible values of P are \u00b11, \u00b15
\nq must divide 4, possible values of q are \u00b11, \u00b12, \u00b14
\nPossible roots are \\(\\pm 1, \\pm \\frac{1}{2}, \\pm \\frac{1}{4}, \\pm 5, \\pm \\frac{5}{2}, \\pm \\frac{5}{4}\\)<\/p>\n

Question 6.
\nThe polynomial x3<\/sup> – kx2<\/sup> + 9x has three real zeros if and only if, k satisfies.
\n(a) |k| \u2264 6
\n(b) k = 0
\n(c) |k| > 6
\n(d) |k| \u2265 6
\nAnswer:
\n(d) |k| \u2265 6
\nHint:
\nx3<\/sup> – kx2<\/sup> + 9x = 0
\n\u21d2 x (x2<\/sup> – kx + 9) = 0
\nx = 0 is one real root. If the remaining roots to be real if the
\nb2<\/sup> – 4ac \u2265 0
\n\u21d2 k2<\/sup> – 36 \u2265 0
\n\u21d2 k2<\/sup> \u2265 36
\n\u21d2 |k| \u2265 6<\/p>\n

\"Samacheer<\/p>\n

Question 7.
\nThe number of real numbers in [0, 2\u03c0] satisfying sin4<\/sup> x – 2sin2<\/sup> x + 1 is ______
\n(a) 2
\n(b) 4
\n(c) 1
\n(d) \u221e
\nAnswer:
\n(c) 1
\nHint:
\nsin4<\/sup> x – 2sin2<\/sup> x + 1 = 0
\n\u21d2 t2<\/sup> – 2t + 1 = 0
\n\u21d2 (t – 1)2<\/sup> = 0
\n\u21d2 t – 1 = 0
\n\u21d2 t = 1
\n\u21d2 sin2<\/sup> x = 1
\n\u21d2 \\(\\frac{1-\\cos 2 x}{2}=1\\)
\n\u21d2 1 – cos 2x = 2
\n\u21d2 cos 2x = cos 0
\n\u21d2 2x = 2n\u03c0
\n\u21d2 x = n\u03c0
\nn = 0, x = 0
\nn = 1, x = \u03c0
\nn = 2, x = 2\u03c0<\/p>\n

\"SamacheerKalvi.Guru\"<\/p>\n

Question 8.
\nIf x3<\/sup> + 12x2<\/sup> + 10ax + 1999 definitely has a positive zero, if and only if _______
\n(a) a \u2265 0
\n(b) a > 0
\n(c) a < 0
\n(d) a \u2264 0
\nAnswer:
\n(c) a < 0
\nHint:
\nIf a < 0, then P(x) = x3<\/sup> + 12x2<\/sup> + 10ax + 1999 has 2 changes of sign.
\n\u2234 P (x) has atmost two positive roots. So a < 0<\/p>\n

Question 9.
\nThe polynomial x3<\/sup> + 2x + 3 has _______
\n(a) one negative and two imaginary zeros
\n(b) one positive and two imaginary zeros
\n(c) three real zeros
\n(d) no zeros
\nAnswer:
\n(a) one negative and two imaginary zeros
\nHint:
\nP(x) = x3<\/sup> + 2x + 3; No positive root.
\nP(-x) = -x3<\/sup> – 2x + 3; Only one change in the sign.
\n\u2234 One negative root.<\/p>\n

Question 10.
\nThe number of positive zeros of the polynomial \"Samacheer is ______
\n(a) 0
\n(b) n
\n(c) <n
\n(d) r
\nAnswer:
\n(b) n<\/p>\n","protected":false},"excerpt":{"rendered":"

You can Download Samacheer Kalvi 12th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations. Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 3.7 Choose the correct or the most suitable answer from the given four alternatives: Question …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[8],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4344"}],"collection":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/comments?post=4344"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4344\/revisions"}],"predecessor-version":[{"id":60168,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4344\/revisions\/60168"}],"wp:attachment":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/media?parent=4344"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/categories?post=4344"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/tags?post=4344"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}