Question

If α,β are the roots of the quadratic equation x2−7x+12=0 , then |α−β|=​

Answer 1

Answer: | α - β | = | ± √1 | = + 1.

Explanation:

Here,

α + β = - b/a = - (- 7)/1 = 7

αβ = c/a = 12/1 = 12

We know,

(a + b)² - (a - b)² = 4ab

=> (α + β)² - (α - β)² = 4αβ

=> (α - β)² = (α + β)² - 4αβ

=> (α - β)² = (7)² - 4(12)

=> (α - β)² = 49 - 48

=> (α - β)² = 1

=> α - β = ± √1 = ± 1.

=> | α - β | = | ± 1 | = 1.

Shortcut:

Use:

$\alpha - \beta = \dfrac{\sqrt{b² - 4ac}}{a} = \dfrac{\sqrt{D}}{a}$.