The zeroes of the polynomial px-2 x2-5 x-3 area 12-3b 12-3c -12-3d 1-12

(b) 12, #160; 3 The zeroes of the polynomial p(x) is given by p(x) = 0. We have: 2x2+5x 3=0 #8658;2x2+6x x 3=0 #8658;2xx+3 1x+3=0 #8658;x+32x 1=0 #86 ...

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Standard IX

Mathematics

Zeroes of a Polynomial

The zeroes of...

Question

The zeroes of the polynomial p(x) = 2x² + 5x − 3 are
(a) $\frac{1}{2}, 3$
(b) $\frac{1}{2}, - 3$
(c) $\frac{- 1}{2}, 3$
(d) $1, \frac{- 1}{2}$

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Solution

(b) $\frac{1}{2}, - 3$

The zeroes of the polynomial p(x) is given by p(x) = 0.
We have:
$2 x^{2} + 5 x - 3 = 0 \Rightarrow 2 x^{2} + 6 x - x - 3 = 0 \Rightarrow 2 x (x + 3) - 1 (x + 3) = 0 \Rightarrow (x + 3) (2 x - 1) = 0 \Rightarrow x = - 3 or x = \frac{1}{2}$
Hence, $\frac{1}{2} and - 3$ are the zeroes of the given polynomial.

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Find the zeroes of the polynomial $p (x) = 2 x^{2} - 5 x - 12$ and verify the relationship between its zeroes and coefficients.

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The zeroes of the polynomial p(x) = 2x2 + 5x − 3 are (a) 12, 3 (b) 12, -3 (c) -12, 3 (d) 1, -12

(b) 12, -3 The zeroes of the polynomial p(x) is given by p(x) = 0. We have: 2x2+5x-3=0⇒2x2+6x-x-3=0⇒2xx+3-1x+3=0⇒x+32x-1=0⇒x=-3 or x=12 Hence, 12 and -3 are the zeroes of the given polynomial.

The zeroes of the polynomial p(x) = 2x² + 5x − 3 are
(a) $\frac{1}{2}, 3$
(b) $\frac{1}{2}, - 3$
(c) $\frac{- 1}{2}, 3$
(d) $1, \frac{- 1}{2}$