Question

If (x - 4) and (x - 1/4) are both factors of ax2 + 5x + b, show that a = b.​

Answer 1

Since, x-4and x-1/4 are the factors of ax2 +5x+b. ax2 +5x+b=(x-4) (x-1/4)

Or, ax2 +5x+b=x (x-1/4) -4(x-1/4)

or, ax2 +5x+b= x^2-1/4x-4x+1

comparing both sides,

we get,

a=1,

b=1

so, a=b

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