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Standard X

Mathematics

Solving a Quadratic Equation by Completing the Square

If a and b ar...

Question

If a and b are the roots of the equation $x^{2} - 5 x + 6 = 0$ , find the value of $(a^{2} - b^{2})$ .

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Solution

The correct option is B $\pm 5$
Given equation is: $x^{2} - 5 x + 6 = 0$
Here, $a + b = 5; a b = 6$
$a^{2} - b^{2} = (a + b) (a - b)$
$= (a + b) \sqrt{{(a + b)}^{2} - 4 a b}$
$= 5. \sqrt{5^{2} - 4 \times 6}$
$= 5. (\pm 1) = \pm 5$

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If a and b are the roots of the equation x2−5x+6=0, find the value of (a2−b2).

The correct option is B ±5Given equation is: x2−5x+6=0Here, a+b=5;ab=6a2−b2=(a+b)(a−b)=(a+b)√(a+b)2−4ab=5.√52−4×6=5.(±1)=±5

If a and b are the roots of the equation $x^{2} - 5 x + 6 = 0$ , find the value of $(a^{2} - b^{2})$ .

The correct option is B $\pm 5$
Given equation is: $x^{2} - 5 x + 6 = 0$
Here, $a + b = 5; a b = 6$
$a^{2} - b^{2} = (a + b) (a - b)$
$= (a + b) \sqrt{{(a + b)}^{2} - 4 a b}$
$= 5. \sqrt{5^{2} - 4 \times 6}$
$= 5. (\pm 1) = \pm 5$