Given: 9x + 1 = 4x2 On rewriting this equation in standard form of the quadratic equation, we get: nbsp;4x2 ndash; 9x ndash; 1 = 0 Comparing this equat ...

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Standard X

Mathematics

Formation of a Quadratic Equation From It's Roots

9 x+1=4 x2

Question

9x + 1 = 4x²

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Solution

Given: 9x + 1 = 4x²
On rewriting this equation in standard form of the quadratic equation, we get:
4x² – 9x – 1 = 0
Comparing this equation with ax² + bx + c = 0, we get:
a = 4, b = –9, c = –1
For the quadratic equation ax² + bx + c = 0, the quadratic formula is $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .
On substituting a = 4, b = –9, c = –1, we get:

$x = \frac{- (- 9) \pm \sqrt{(- 9)^{2} - 4 (4) (- 1)}}{2 (4)} = \frac{9 \pm \sqrt{81 + 16}}{2 (4)} = \frac{9 \pm \sqrt{97}}{8} = \frac{9 + \sqrt{97}}{8}, \frac{9 - \sqrt{97}}{8} Thus, the solution of the given quadratic equation is = \frac{9 + \sqrt{97}}{8}, \frac{9 - \sqrt{97}}{8} .$

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