Answer:
The roots of the equations are x ≈ -5.26 and x ≈ 0.76 .
Option (d) is correct.
Step-by-step explanation:
Formula for the roots is given by .
\(x = \frac{-b \pm \sqrt{b^{2} -4ac}}{2a}\)
As the equation in the form
\(2x^{2} + 9x - 8 = 0\)
As the equation in the form ax² + bx + c = 0
a = 2, b= 9 , c = -8
Put in the formula
\(x = \frac{-9 \pm \sqrt{9^{2} -4\times 2\times -8}}{2\times 2}\)
\(x = \frac{-9 \pm \sqrt{81 + 64}}{4}\)
\(x = \frac{-9 \pm \sqrt{145}}{4}\)
\(\sqrt{145} = 12.04\)
Thus First roots be
\(x = \frac{-9 - 12.04}{4}\)
\(x = \frac{-21.04}{4}\)
x ≈ -5.26
The second root be
\(x = \frac{-9 + 12.04}{4}\)
\(x = \frac{3.04}{4}\)
x ≈ 0.76
Therefore the roots of the equations are x ≈ -5.26 and x ≈ 0.76 .
Option (d) is correct.
