Question

If x2+ax+b is a perfect square prove that a2=4b.​

Answer 1

Step-by-step explanation:

x2+ax+b

=(x)2+2(a2)x+(b√)2

Now, above quadratic polynomial will be a perfect square only if the coefficient of x is ±2 times the square root of product of coefficient of x2 & constant as follows

a=±21⋅b−−−√

a=±2b√

a2=(±2b√)2

a2=4b

Answer 2

Answer:

x2+ax+b

=(x)2+2(a2)x+(b√)2

Now, above quadratic polynomial will be a perfect square only if the coefficient of x is ±2 times the square root of product of coefficient of x2 & constant as follows

a=±21⋅b−−−√

a=±2b√

a2=(±2b√)2

a2=4b