Question

If a and b are real and a is not equal to b then show that the roots of the equation (a-b) x2+5(a+b) x-2(a-b) =0

Answer 1

Answer:-

Given:- (a-b)x² + 5( a + b )x - 2( a-b) is an equation where( a ≠ b )

To prove:- The roots of the equation are real and unequal .

Proof:-

Here,

↦a = ( a - b )

↦b = 5(a + b )

↦c = -2(a-b)

For real and Unequal roots ,

↦D > 0

⇒b² - 4ac

⇒[5(a + b ) ]² - 4 × ( a - b ) [ -2 (a - b)]

⇒ 25(a + b )² - 4 × ( a - b ) [ -2 (a - b)]

⇒25(a + b)² + 8(a - b)² >0 [ since , sum of the square of two number is greater than 0 ]

. ° . The Roots are real and unequal .(proved)