Match the following columns-1-c- Column I 1-c- Column II a The polynomial whose zeros are 2 and -3 is - - - p x2-4 x-1 b The polynomial whose zeros are 2-3 and 2-3 is - q x 2-23 x-2 c The polynomial whose zeros are 32 and -12 is - r x2-x-6 d The polynomial whose zeros are 3-1 and 3-1 s 4 x2-4 x-3

(a) #160; #945;=2 #160;and #160; #946;= 3 #945;+ #946;=2+( 3)= 1 #945; #946;=2 #215;( 3)= 6 #8756; #160;The #160;required #160;polyn ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Relations between Roots and Coefficients : Higher Order Equations

Match the fol...

Question

Match the following columns:

Column I Column II

(a) The polynomial whose zeros
are 2 and −3 is ......... . (p) x²− 4x + 1

(b) The polynomial whose zeros are $(2 + \sqrt{3}) and (2 - \sqrt{3})$ is ......... . (q) $x^{2} - 2 \sqrt{3} x + 2$

(c) The polynomial whose zeros
are $\frac{3}{2} and - \frac{1}{2}$ is ......... . (r) x² + x − 6

(d) The polynomial whose zeros
are $(\sqrt{3} + 1) and (\sqrt{3} - 1)$ (s) 4x²− 4x − 3

Open in App

Solution

$(a) α = 2 and β = - 3 α + β = 2 + (- 3) = - 1 αβ = 2 \times (- 3) = - 6 ∴ The required polynomial will be x^{2} - (α + β) + αβ = x^{2} + x - 6 . (b) α = 2 + \sqrt{3} and β = 2 - \sqrt{3} α + β = 2 + \sqrt{3} + 2 - \sqrt{3} = 4 α β = (2 + \sqrt{3}) (2 - \sqrt{3}) = 4 - 3 = 1 ∴ The required polynomial will be x^{2} - (α + β) + αβ = x^{2} - 4 x + 1 . (c) α = \frac{3}{2} and β = \frac{- 1}{2} α + β = \frac{3}{2} - \frac{1}{2} = 1 αβ = \frac{- 3}{4} \begin{array}{l} ∴ R equired polynomial = x^{2} - (α + β) + αβ = x^{2} - x - \frac{3}{4}, i .e ., 4 x^{2} - 4 x - 3 \end{array} (d) α = \sqrt{3} + 1 and β = \sqrt{3} - 1 α + β = 2 \sqrt{3} α β = 3 - 1 = 2 ∴ T he required polynomial is x^{2} - (α + β) + α = x^{2} - 2 \sqrt{3} x + 2 . Thus, the correct matches are (a) - (r), (b) - (p), (c) - (s) and (d) - (q) .$

Suggest Corrections

Similar questions

Q. Assertion :Zeroes of

f (x) = x^{2} - 4 x - 5

are 5,-1 Reason: The polynomial whose zeroes are

2 + \sqrt{2}, 2 - \sqrt{3}

x^{2} - 4 x + 7

α

and

β

are the zeros of the polynomial

x^{2} + 4 x + 3

. The polynomial whose zeros are

1 + \frac{β}{α}

and

1 + \frac{α}{β}

Verify that
(i) 1 and 2 are the zeros of the polynomial, $p (x) = x^{2} - 3 x + 2$ .
(ii) 2 and -3 are the zeros of the polynomial, $q (x) = x^{2} + x - 6.$
(iii) 0 and 3 are the zeros of the polynomial, $r (x) = x^{2} - 3 x$ .

Q. Match the following columns:

Column I	Column II
(a) $2 x^{2} - 7 x + 5 = 0$	(p) Real and equal
(b) $3 x^{2} - 2 \sqrt{6} x + 2 = 0$	(q) Real, distinct and irrational
(c) $9 x^{2} - 10 x + 15 = 0$	(r) Real distinct and rational
(d) $\sqrt{3} x^{2} + 2 \sqrt{2} x - 2 \sqrt{3} = 0$	(s) Imaginary

Q. Match the following columns:

Column I	Column II
(a) $\sqrt[3]{6}$	(p) terminates after 4 places of decimal
(b) $0.3465$	(q) is irrational
(c) $\frac{1234}{625}$	(r) terminates after 3 places of decimal
(d) $\frac{3416}{125}$	(s) is a non-terminating and repeating decimal

Join BYJU'S Learning Program

Column I	Column II
(a) The polynomial whose zeros are 2 and −3 is ......... .	(p) x²− 4x + 1
(b) The polynomial whose zeros are $(2 + \sqrt{3}) and (2 - \sqrt{3})$ is ......... .	(q) $x^{2} - 2 \sqrt{3} x + 2$
(c) The polynomial whose zeros are $\frac{3}{2} and - \frac{1}{2}$ is ......... .	(r) x² + x − 6
(d) The polynomial whose zeros are $(\sqrt{3} + 1) and (\sqrt{3} - 1)$	(s) 4x²− 4x − 3