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