VJesus12 wrote: ↑

Tue Aug 18, 2020 8:35 am

What are the roots of the quadratic equation \(x^2 + bx + c = 0\) if the roots are distinct and at equal distance from \(5\) on the number line?

(1) The product of the roots of the equation \(x^2 + bx + c = 0\) is \(21.\)

(2) \(x - 7\) is a factor of the expression \(x^2 + bx + c.\)

Answer: D

Source: e-GMAT

For the quad equation x^2 + bx + c = 0 let the distance of the root of the equation from 5 be d. Hence, the two roots are (5-d) and (5+d)
the sum of the roots = 10
therefore, -b/a=10
a is 1 (coefficient of x)
-b=10
b=10

statement 1 product of the roots is 21
c/a =21
c=21
x^2-10x+21=0 we can solve and find the value of the roots

statement 2
x-7 is a factor, therefore, x=7 satisfies the equation and is one of the roots
5 + d = 7 so d = 2 and hence the other root is 5 – d = 3. or
5 – d = 7 so, d = -2 and hence the other root is 5 +(-2) = 3

In both cases, we get the same values of the roots.

Sufficient

Therefore D