Question 1 (i)

Find the roots of the quadratic equations by using the quadratic formula in the following question $2 x^{2} - 3 x - 5 = 0$ .

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Solution

Given equation is $2 x^{2} - 3 x - 5 = 0$
On comparing with $a x^{2}$ + bx + c = 0, we get
a = 2, b = - 3 and c = - 5
by quadratic formula, $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
$x = \frac{- (- 3) \pm \sqrt{(- 3)^{2} - 4 (2) (- 5)}}{2 (2)} = \frac{3 \pm \sqrt{9 + 40}}{4}$
$= \frac{3 \pm \sqrt{49}}{4} = \frac{3 \pm 7}{4} = \frac{10}{4}, \frac{- 4}{4} = \frac{5}{2}, - 1$
So, $\frac{5}{2}$ and – 1 are the roots of the given equation.

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