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Find out the zeroes of the polynomial $2 x 2 + 72 x + 34$ .

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\frac{- 1}{4}, \frac{- 3}{4}

\frac{- 1}{4}, \frac{- 3}{4}

\frac{- 1}{2}, \frac{- 3}{4}

\frac{- 1}{3}, \frac{- 3}{4}

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Detailed Solution

Given quadratic polynomial is

2 x 2 + 72 x + 34 .

Then,

2 x^{2} + \frac{7}{2} x + \frac{3}{4} = 0

\Rightarrow 8 x^{2} + 14 x + 3 = 0

\Rightarrow 8 x^{2} + 12 x + 2 x + 3 = 0

\Rightarrow 4 x (2 x + 3) + 1 (2 x + 3) = 0

\Rightarrow (4 x + 1) (2 x + 3) = 0

So,

⇒ 4 x + 1 = 0 ∴ x = − 14

And,

⇒ 2 x + 3 = 0 ∴ x = − 32

Therefore, the zeroes are

x = − 14

and

x = − 32 .

Hence, option (2) is correct.

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