If - - are the roots of the equation x 2-5 x -6-0- the value of -2-2 is-A- - 5B- - 13C- - 6D- - 7

The correct option is A ±5Given quadratic equation x^2 5x + 6 =0 ∴ a = 1, b = 5, c = 6 ∴ x = b ±√(b^2 4ac)/2a ⇒ x = ( 5) ±√(( 5)^2 4(1)(6))/2(1) ⇒ x ...

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Byju's Answer

Standard X

Mathematics

Applications of Second Degree Equations

If α, β are t...

Question

If $α$ , $β$ are the roots of the equation $x^{2} - 5 x + 6 = 0$ , the value of $α^{2} - β^{2}$ is:

\pm 5

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Solution

The correct option is A $\pm 5$
Given quadratic equation $x^{2} - 5 x + 6 = 0$
$∴$ a = 1, b = -5, c = 6

$∴ x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
$\Rightarrow x = \frac{- (- 5) \pm \sqrt{(- 5)^{2} - 4 (1) (6)}}{2 (1)}$
$\Rightarrow x = \frac{5 \pm \sqrt{25 - 24}}{2}$
$\Rightarrow x = \frac{5 \pm 1}{2}$
$\Rightarrow x = 3, 2$

If $α$ , $β$ is 3,2 , then $α^{2} - β^{2} = 9 - 4 = 5$
If $α$ , $β$ is 2,3 , then $α^{2} - β^{2} = 4 - 9 = - 5$

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If α, β are the roots of the equation x2−5x+6=0, the value of α2−β2 is:

The correct option is A ±5Given quadratic equation x2−5x+6=0 ∴ a = 1, b = -5, c = 6 ∴x=−b±√b2−4ac2a ⇒x=−(−5)±√(−5)2−4(1)(6)2(1) ⇒x=5±√25−242 ⇒x=5±12 ⇒x=3,2 If α, β is 3,2 , then α2−β2=9−4=5 If α, β is 2,3 , then α2−β2=4−9=−5

If $α$ , $β$ are the roots of the equation $x^{2} - 5 x + 6 = 0$ , the value of $α^{2} - β^{2}$ is: