Question

if a+b+c=0 and ax^2+bx+c=0 has equal roots then both roots are equal to:
(A) 0
(B) 1
(C) -1
(D) none of these ​

Answer 1

Given that a+b+c = 0

and ax^2+bx+c=0 has equal roots

If we put x=1 we get a+b+c = 0 which is given.

So x=1 is a root.

Since both roots are equal, the roots are 1.

Answer 2

GIVEN:

• a + b + c = 0------------- ( 1 )
• ax² + bx + c = 0

TO FIND:

• Roots of ax² + bx + c = 0

SOLUTION:

p(x) = ax² + bx + c = 0

That means p(x) = 0

Putting x = 1

→ p(1) = a(1)² + b(1) + c

→ p(1) = a + b + c

→ a + b + c = 0 (°.° Equation 1)

Hence, roots of equation ‘ax² + bx + c = 0’ are x = (1 , 1)

MORE INFO:

→ (a + b)² = a² + b² + 2ab

→ (a - b)² = a² + b² - 2ab

→ a² - b² = (a + b)(a - b)

→ a² + b² = (a + b)² - 2ab

Quadratic equation formula

→ x = -b ± √b² - 4ac/2a