Find the roots of the equation $16 x^{2} - 27 x - 10 = 0$ .

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Solution

$16 x^{2} - 27 x - 10 = 0$
Compare the given equation with $a x^{2} + b x + c = 0$ we get,
$a = 16, b = - 27, c = - 10$
The roots can be found using the formula
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
$∴ x = \frac{27 \pm \sqrt{(27)^{2} - 4 \times 16 \times (- 10)}}{2 \times 16}$

$= \frac{27 \pm \sqrt{1369}}{32} = \frac{27 \pm 37}{32} = \frac{64}{32}, \frac{- 10}{32}$
$∴$ The roots are $\frac{- 5}{16}$ and $2$ .

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Find the roots of the equation 16x2−27x−10=0.

16x2−27x−10=0Compare the given equation with ax2+bx+c=0 we get,a=16,b=−27,c=−10The roots can be found using the formulax=−b±√b2−4ac2a∴x=27±√(27)2−4×16×(−10)2×16=27±√136932=27±3732=6432,−1032∴ The roots are −516 and 2.

Find the roots of the equation $16 x^{2} - 27 x - 10 = 0$ .