Question

for what value of k is the polynomial p(x)=2x³-kx²+5x+9 exactly divisible by x+2

Answer 1

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x + 2 = 0

x = -2

p(x) = 2x³-kx²+5x+9

p (-2) = 2×(-2)³ - k(-2)² + 5(-2) + 9

= 2×(-8) - 4k - 10 + 9

= - 16 - 4k - 10 + 9

= -35 - 4k

35 = -4k

35/ (-4) = k

HENCE , VALUE OF K = -35/4

Answer 2

Given

We have given a cubic polynomial 2x³-kx²+5x+9

And zeroes x+2

To find

we have to find the value of K

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Since ,we have given a polynomial 2x³-kx²+5x+9

One zeroes is given x+2

So,value of x will be =>x+2=0 => x = -2

Put value of x into the given equation

=>2x³-kx²+5x+9

Put x = -2 and makes the Equation equals to zero:

=> 2(-2)³-k(-2)²+5(-2)+9=0

=>2(-8)-k(4)-10+9=0

=>-16-4k-1=0

=>-16-1-4k= 0

=>-17-4k=0

=>-4k= 17

=> k = -17/4

Check:

➛2x³-kx²+5x+9=0

➛2(-2)³-(-17/4)(-2)²+5(-2)+9

➛-16+17/4×4-10+9

➛-16+17-1

➛1-1=0