Question

if x=2 is a zero of the polynomial 2x2×3x_p then the value of p is ​

Answer 1

Correct Question

• If 2 is a zero of the polynomial 2x² + 3x - p , then find the value of p.

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Given

• p(x) = 2x² + 3x - p
• Zero of the polynomial is 2.

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To find

• Value of p.

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Solution

• We have one zero of the polynomial, let put the value in the polynomial.

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⠀⠀⠀⠀❍ x = 2

$\tt:\implies\: \: \: \: \: \: \: \: {p(x) = 2x^2 + 3x - p}$

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$\tt:\implies\: \: \: \: \: \: \: \: {p(2) = 2(2)^2 + 3(2) - p}$

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$\tt:\implies\: \: \: \: \: \: \: \: {p(2) = 2(4) + 6 - p}$

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$\tt:\implies\: \: \: \: \: \: \: \: {p(2) = 8 + 6 - p}$

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$\tt:\implies\: \: \: \: \: \: \: \: {p(2) = 14 - p}$

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⠀⠀❍ Since 2 is the zero of polynomial

$\boxed{\sf{\orange{p(2) = 0}}}$

$\tt\longmapsto{14 - p = 0}$

$\tt\longmapsto{-p = 14}$

$\bf\longmapsto{p = -14}$

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Hence,

• The value of p is -14.

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