Question

$a,b\in R,a\ne b$ roots of equation $(a-b)x^2+5(a+b)x-2(a-b)=0$are

• A. Real and distinct
• B. Complex
• C. Real and equal
• D. None

Answer 1

The correct option is A

Real and distinct

Explanation for the correct option:

Step 1: Find the discriminant of the given quadratic equation.

We have been given a quadratic equation $(a-b)x^2+5(a+b)x-2(a-b)=0$

We need to find the nature of the roots of a given quadratic equation.

The discriminant for a given quadratic equation would be,

$$\begin{gathered} =(5{(a+b))}^2-[4\times (a-b)\times (-2(a-b\left)\right)] \\ =25{(a+b)}^2+8{(a-b)}^2 \end{gathered}$$

Step 2: Using the discriminant value, decide the nature of the roots.

Since, $a\ne b$ ${(a+b)}^2,{(a-b)}^2>0$

$\Rightarrow 25{(a+b)}^2+8{(a-b)}^2>0$

This means the roots of the above quadratic equation are real and distinct.

Therefore, option (A) is the correct answer.