Find that c

Algebra Level 2

If x − 2 x-2 is a factor of the polynomial 4 x 2 − 77 x + c 4x^{2} - 77x + c , find the value of c c .


The answer is 138.

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Ir J by IR J , 21, Philippines

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2 solutions

4 x 2 − 77 x + c x − 2 = 4 x − 69 \dfrac{4x^2-77x+c}{x-2}=4x-69

4 x 2 − 77 x + c = ( 4 x − 69 ) ( x − 2 ) 4x^2-77x+c=(4x-69)(x-2)

4 x 2 − 77 x + c = 4 x 2 − 77 x + 138 4x^2-77x+c=4x^2-77x+138

c = 138 c=\boxed{138}

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Zakir Husain
May 16, 2020

As x-2 is it's factor

=> 2 is its root by factor theorem

=> 4 ( 2 2 ) − 77 ( 2 ) + c = 0 4(2^{2})-77(2)+c=0

=> 16 − 154 + c = 0 16-154+c=0

=> c = 154 − 16 = 138 c=154-16=\boxed{138}

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