Zero of the polynomial $p (x) = x^{2} + x - 6$ are
(a) 2,3
(b) -2,3
(c) 2,-3
(d) -2,-3

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Solution

Given equation
$x^{2} + x - 6$
Using factorisation method

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

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

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

So, zeroes of the polynomial are:

$x - 2 = 0$

$\Rightarrow$ x =2

$(x + 3) = 0$

$\Rightarrow$ x = -3

Hence, the correct option is 2, -3
Hence, correct answer is option (C).

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Similar questions

Q. The zeroes of the polynomial p(x) = x² + x − 6 are
(a) 2, 3
(b) −2, 3
(c) 2, −3
(d) −2, −3

The domain of the function $f (x) = \sqrt{5 | x | - x^{2} - 6}$ is

Q. Verify that:
(i) 4 is a zero of the polynomial p(x) = x − 4.
(ii) −3 is a zero of the polynomial p(x) = x − 3.
(iii)

- \frac{1}{2}

is a zero of the polynomial p(y) = 2y + 1.
(iv)

\frac{2}{5}

is a zero of the polynomial p(x) = 2 − 5x.
(v) 1 and 2 are the zeros of the polynomial p(x) = (x − 1)(x − 2).
(vi) 0 and 3 are the zeros of the polynomial p(x) = x² − 3x.
(vii) 2 and −3 are the zeros of the polynomial p(x) = x² + x − 6.

Q. The domain of the function

f (x) = \sqrt{5 |x| - x^{2} - 6}

is

(a) (−3, − 2) ∪ (2, 3)
(b) [−3, − 2) ∪ [2, 3)
(c) [−3, − 2] ∪ [2, 3]
(d) None of these

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, $r (x) = x^{2} - 3 x$ .

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Zero of the polynomial p(x)=x2+x−6 are (a) 2,3 (b) -2,3 (c) 2,-3 (d) -2,-3

Given equationx2+x–6 Using factorisation method x2+3x−2x–6 x(x+3)−2(x+3) (x−2)(x+3) So, zeroes of the polynomial are: x−2=0 ⇒ x =2 (x+3)=0 ⇒ x = -3 Hence, the correct option is 2, -3 Hence, correct answer is option (C).

Zero of the polynomial $p (x) = x^{2} + x - 6$ are
(a) 2,3
(b) -2,3
(c) 2,-3
(d) -2,-3