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

The given polynomial is nbsp;p(x) = nbsp;x2 nbsp;+ nbsp;x nbsp; ndash; 6. Putting nbsp;x = 2 in nbsp;p(x), we get p(2) = nbsp;22 nbsp;+ ...

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Standard IX

Mathematics

Zeroes of a Polynomial

The zeros of ...

Question

The zeros 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

The given polynomial is p(x) = x² + x – 6.

Putting x = 2 in p(x), we get

p(2) = 2² + 2 – 6 = 4 + 2 – 6 = 0

Therefore, x = 2 is a zero of the polynomial p(x).

Putting x = –3 in p(x), we get

p(–3) = (–3)² – 3 – 6 = 9 – 9 = 0

Therefore, x = –3 is a zero of the polynomial p(x).

Thus, 2 and –3 are the zeroes of the given polynomial p(x).

Hence, the correct answer is option (c).

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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 zeros of the polynomial p(x) = x2 + x – 6 are (a) 2, 3 (b) –2, 3 (c) 2, –3 (d) –2, –3

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