Question

Find all the integral values of a for which the quadratic equation(x-a)(x-10)+1=0 has integral roots ....plzzz answer this...

Answer 1

Given:

quadratic equation(x-a)(x-10)+1=0 has integral roots.

To find:

the integral values of a.

Solution:

1) The equation has the equal roots means that the discriminant value must be equal to zero.

2) If we solve the given equation we get,

(x-a)(x-10)+1=0

x² -(a+10)x +10a+1=0

3) Discriminant:

• $\sqrt{b^{2}-4ac}$ = 0

• $\sqrt{(a+10)^{2} - 4(10a+1)}$ = 0

• $\sqrt{a^{2}-20a +96 }$ = 0

• $a^{2}-20a +96$ = 0

• (a-12)(a-8) = 0

• a = 12 , 8

the integral values of a are 12 and 8