Question

value of k if y-1 is a factor of p(y)=y^2+y+k​

Answer 1

Answer

k = - 2

Given

y - 1 is a factor of p(y) = y² + y + k​

To Find

Value of k

Key point

A/c to factor theorem ,

If x - q is a factor  of the polynomial of p(x) , then

p(q) = 0

Solution

Given polynomial , p(y) = y² + y + k and

y - 1 is a factor of p(y)

⇒ y - 1 = 0

⇒ y = 1 is a factor of p(y)

So ,

⇒ p(y) = 0

⇒ p(1) = 0

⇒ (1)² + (1) + k = 0

⇒ 1 + 1 + k = 0

⇒ 2 + k = 0

⇒ k = -2

Answer 2

$\bf\huge\blue{\underline{\underline{ Question : }}}$

Value of k if y - 1 is a factor of p(y) = y² + y + k.

$\bf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• (y - 1) is the factor of the polynomial p(y) = y² + y + k = 0

★ To find,

• Value of the k.

★ Let,

According to the question,

◼ (y - 1) is a factor of p(y). So, one of the roots of the polynomial is 1.

◼ Now, substitute the value of y in the polynomial p(y).

$\bf\:\implies (1)^{2} + (1) + k = 0$

$\bf\:\implies 1 + 1 + k = 0$

$\bf\:\implies 2 + k = 0$

$\bf\:\implies k = 0 - 2$

$\bf\:\implies k = - 2$

$\underline{\boxed{\rm{\purple{\therefore The\:value\:of\:k\:is\:-2}}}}\:\orange{\bigstar}$

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