Question

if 5 is a zero of x^3+kx^2x+8. find k​

Answer 1

$\underline{\red{\sf{\large{Question:-}}}}$

5 is a zero of x³ + kx² + x + 8. Find k

$\underline{\red{\sf{\large{Answer:-}}}}$

$\underline{\boxed{\bf{\blue{Zero\:of\:a\:polynomial:-}}}}$

Suppose p(x) is a polynomial. If p(a) =0, then a is called a zero of the polynomial p(x)

p(a) means you substitute the value of a as x in the expression.

$\huge{\mathtt{\underline{So}}}$

p(x) = x³ + kx² + x + 8

Here a is 5. 5 is the zero

p(5) = 5³ + (k * 5²) + 5 + 8 = 0

$\implies$ p(5) = 125 + 25k + 13 = 0

$\implies$ p(5) = 25k + 138 = 0

$\implies$ p(5) = 25k = 0 - 138 = -138

$\implies$ p(5) = k = -138/25

$\large{\boxed{\bf{\green{\boxed{k\:=\:-138/25}}}}}$

$\huge{\mathtt{\underline{NOTE:-}}}$

If you meant 5 is a zero of x³ + kx² + 2x + 8

Then,

p(5) = 5³ + (k * 5²) + (2 * 5) + 8 = 0

$\implies$ 125 + 25k + 10 + 8 = 0

$\implies$ 25k + 143 = 0

$\implies$ 25k = 0 - 143 = -143

$\implies$ k = -143/25

$\large{\boxed{\bf{\green{\boxed{k\:=\:-143/25}}}}}$

Answer 2

K = -143 / 25

Step-by-step explanation:

p(x) =x^3 + kx^2 +2x +8

substituting x

therefore , p(5)= (5)^3 + k(5)^2 + 2(5) + 8

= 125 + 25k +10 + 8

= 143 + 25k

Since 5 is a zero of p(x) , it is a factor of p(x)

Hence , p(x) = 0

therefore , 143 + 25k =0

25k = - 143

K = - 143 /25

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