Question

solve the equation
$2x { }^{2} + 13x + 15 = 0$
by factorisation method,by completing the square method and by using the formula method.verify that you will get the same roots every time.​

Answer 1

Mate here is your answer please mark braineliest

FACTORIZATION METHOD

$2 {x}^{2} + 13x + 15 = 0 \\ = > 2 {x}^{2} + 10x + 3x + 15 = 0 \\ = > 2x(x + 5) + 3(x + 5) = 0 \\ = > (2x + 3)(x + 5) = 0 \\ = > x = - \frac{3}{2} or \: x = - 5$

COMPLETING SQUARE METHOD

${2x}^{2} + 13x + 15 = 0 \\ = > \frac{2 {x}^{2} }{2} + \frac{13}{2} x + \frac{15}{2} = \frac{0}{2} \\ = > {x}^{2} + \frac{13}{2} x = - \frac{15}{2} \\ = > {x}^{2} + 2 \times \frac{13}{4} \times x + (\frac{13}{4}) ^{2} = - \frac{15}{2} + ( \frac{13}{4} ) ^{2} \\ = > {(x + \frac{13}{4}) }^{2} = - \frac{15}{2} + \frac{169}{16} \\ = > {(x + \frac{13}{4}) }^{2} = \frac{ - 120 + 169}{16} \\ = > x + \frac{13}{4} = \frac{ + }{} \sqrt{ \frac{49}{16} } \\ = > x = \frac{7}{4} - \frac{13}{4} or \: - \frac{7}{4} - \frac{13}{4} \\ = > x = - \frac{6}{4} = - \frac{3}{2} \: \: or \: \: - \frac{20}{4} = - 5$

FORMULA METHOD

HERE , a= 2 , b= 13 , c= 15

$d = {b}^{2} - 4ac \\ = > d = {13}^{2} - 4 \times 2 \times 15 \\ = > d = 169 - 120 \\ = > d = 49 \\ = > \sqrt{d} = 7$

So, By quadratic formula,

$x = \frac{ - b \frac{ + }{} \sqrt{d} }{2a} \\ = > x = \frac{ - 13 + 7}{2 \times 2} \: or \: \frac{ - 13 - 7}{2 \times 2} \\ = > x = \frac{ - 6}{2 \times 2} = - \frac{3}{2} \: or \: \frac{ - 20}{2 \times 2} = - 5$