12 abx 2-9 a 2-8 b 2 x -6 ab -0- where a - 0 and b - 0

Given:12abx2 #160; #8722; #160;(9a2 #160; #8722; #160;8b2)x #160; #8722; #160;6ab #160;= #160;0 #160; #160; #160; #160; #160;On ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Nature of Roots

12 abx 2-9 a ...

Question

$12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0$ , where a $\neq$ 0 and b $\neq$ 0

Open in App

Solution

$Given: 12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0 On c omparing it with A x^{2} + B x + C = 0, we get: A = 12 a b, B = - (9 a^{2} - 8 b^{2}) and C = - 6 a b Discriminant D is given by : D = B^{2} - 4 A C = {[- (9 a^{2} - 8 b^{2})]}^{2} - 4 \times 12 a b \times (- 6 a b) = 81 a^{4} - 144 a^{2} b^{2} + 64 b^{4} + 288 a^{2} b^{2} = 81 a^{^{4}} + 144 a^{2} b^{2} + 64 b^{4} = {(9 a^{2} + 8 b^{2})}^{2} > 0 Hence, the roots of the equation are equal. Roots α and β are given by: α = \frac{- B + \sqrt{D}}{2 A} = \frac{- [- (9 a^{2} - 8 b^{2})] + \sqrt{{(9 a^{2} + 8 b^{2})}^{2}}}{2 \times 12 a b} = \frac{9 a^{2} - 8 b^{2} + 9 a^{2} + 8 b^{2}}{24 a b} = \frac{18 a^{2}}{24 a b} = \frac{3 a}{4 b} β = \frac{- B - \sqrt{D}}{2 A} = \frac{- [- (9 a^{2} - 8 b^{2})] - \sqrt{{(9 a^{2} + 8 b^{2})}^{2}}}{2 \times 12 a b} = \frac{9 a^{2} - 8 b^{2} - 9 a^{2} - 8 b^{2}}{24 a b} = \frac{- 16 b^{2}}{24 a b} = \frac{- 2 b}{3 a} Thus, the roots of the equation are \frac{3 a}{4 b} and \frac{- 2 b}{3 a} .$

Suggest Corrections

Similar questions

Q. Evaluate

12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0

, where

a \neq 0

and

b \neq 0

12 a b x^{2} - ({9 a}^{2} - {8 b}^{2}) x - 6 a b = 0

Q. Solve for

x

12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0

Solve each of the following quadratic equations:
$12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0, w h e r e a \neq 0 a n d b \neq 0$

Join BYJU'S Learning Program

12abx2-(9a2-8b2)x-6ab=0, where a≠0 and b≠0

$12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0$ , where a $\neq$ 0 and b $\neq$ 0