The zeroes of the polynomial px-x2-x-6 area 2-3b -2-3c 2-3d -2-3

(c) 2, minus;3 The zeroes of the polynomial nbsp;p(x) is given by nbsp;p(x) = 0. We have: x2+x 6=0 #8658;x2+3x 2x 6=0 #8658;xx+3 2x+3=0 #8658;x+3x ...

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Standard IX

Mathematics

Zeroes of a Polynomial

The zeroes of...

Question

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

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Solution

(c) 2, −3

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

Hence, 2 and $-$ 3 are the zeroes of the given polynomial.

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Similar questions

Zero of the polynomial $p (x) = x^{2} + x - 6$ 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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The zeroes of the polynomial p(x) = x2 + x − 6 are (a) 2, 3 (b) −2, 3 (c) 2, −3 (d) −2, −3

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

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

(c) 2, −3

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

Hence, 2 and $-$ 3 are the zeroes of the given polynomial.