The zeros of the polynomial px-2x2-5x-3 are a 1-2-3 b 1-2-3 c -1-2-3 d 1-1-2

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Standard IX

Mathematics

Factorisation of Quadratic Polynomials- Middle Term Splitting

The zeros of ...

Question

The zeros of the polynomial $p (x) = 2 x^{2} + 5 x - 3$ 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

$p (x) = 2 x^{2} + 5 x - 3$

Now, factorise the $2 x^{2} + 5 x - 3$

$2 x^{2} + 5 x - 3$

$2 x^{2} + 6 x - x - 3$

$2 x (x + 3) - 1 (x + 3)$

$(2 x - 1) (x + 3)$

So, zeroes of the polynomial are:

$(2 x - 1) (x + 3)$ = 0

x = $\frac{1}{2}$ , -3

Hence, the correct option is $\frac{1}{2}, - 3$ i.e. (b).

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Similar questions

Q. Verify that 3, -2, 1 are the zeroes of the cubic polynomial

p (x) = x^{3} - 2 x^{2} - 5 x + 6

The zeros of the polynomial $p (x) = 3 x^{2} - 1$ are
(a) $\frac{1}{3}$ and 3
(b) $\frac{1}{\sqrt{3}}$ and $\sqrt{3}$
(c) $\frac{- 1}{\sqrt{3}}$ and $\sqrt{3}$
(d) $\frac{1}{\sqrt{3}}$ and $\frac{- 1}{\sqrt{3}}$

Q. If

- \frac{1}{2}

is a zero of polynomial

p (x) = 2 x^{2} - 5 x - k

then find the value of

k

Find the zeroes of the polynomial of p(x) = 2x² - 1

Q. Verify whether the following are zeroes of the polynomial, indicated against them.
(i) p(x) = 3x + 1, x =

- \frac{1}{3}

(ii)

p (x) = 5 x - π, x = \frac{4}{5}

(iii)

p (x) = x^{2} - 1, x = 1, - 1

(iv) p(x) = (x +1) (x -2), x = - 1, 2

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

p(x)=2x2+5x−3 Now, factorise the 2x2+5x−3 2x2+5x−3 2x2+6x−x−3 2x(x+3)−1(x+3) (2x−1)(x+3) So, zeroes of the polynomial are: (2x−1)(x+3) = 0 x = 12, -3 Hence, the correct option is 12,−3 i.e. (b).

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