Question

For which value of `a` polynomial (x - 4)^2 + (2a - 373)^2 will have equal zeroes?​

Answer 1

Answer:

So, the value of a is = 373/2, for which the polynomial will have two equal zeroes

Step-by-step explanation:

We have to find the value of 'a' for which the polynomial (x-4) ^2 +(2a-373) ^2 has equal zeroes, that is,

(x-4) ^2 + (2a-373) ^2 = 0 , this equation has two equal value of x

Now the equation will have two equal roots if the discriminate of the equation will be zero,

Now, (x-4) ^2+(2a-373) ^2=0

=> x^2 -8x +16 + (2a-373) ^2 = 0

The discriminate of the equation is

= (-8) ^2 -4×1×(16+(2a-373) ^2)

= 64 - 64 -4(2a-373) ^2

= -4(2a-373) ^2

Now for two equal roots,

-4(2a-373) ^2 = 0

=> (2a-373) ^2 = 0

=> 2a-373= 0

=> 2a = 373

=> a = 373/2

Therefore when a = 373/2, the polynomial will have two equal zeroes