The zeroes of the polynomial 4x2 + 5√2x – 3 are (a) -3√2, √2�

1.	The zeroes of the polynomial 4x2 + 5√2x – 3 are (a) -3√2, √2 (b) -3√2, \(\frac{\sqrt2}2\) (c) \(\frac{-3}{\sqrt2}\), \(\frac{\sqrt2}4\)(d) none of these
Answer» (c) \(\frac{-3}{\sqrt2}\), \(\frac{\sqrt2}4\) Let f(x) = 4x² + 5√2x – 3 = 0 ⇒ 4x² + 6√2x – √2x – 3 = 0 ⇒ 2√2x(√2x + 3) –1 (√2x + 3) = 0 ⇒ (√2x + 3) (2√2x – 1) = 0 ⇒ x = – \(\frac{3}{\sqrt2}\) or x = \(\frac{1}{2\sqrt2}\) ⇒ x = – \(\frac{3}{\sqrt2}\)or x = \(\frac{1}{2\sqrt2}\) x \(\frac{\sqrt2}{\sqrt2}\) = \(\frac{\sqrt2}4\)

The zeroes of the polynomial 4x2 + 5√2x – 3 are (a) -3√2, √2 (b) -3√2, \(\frac{\sqrt2}2\) (c) \(\frac{-3}{\sqrt2}\), \(\frac{\sqrt2}4\)(d) none of these

Answer»

(c) \(\frac{-3}{\sqrt2}\), \(\frac{\sqrt2}4\)

Let f(x) = 4x² + 5√2x – 3 = 0

⇒ 4x² + 6√2x – √2x – 3 = 0

⇒ 2√2x(√2x + 3) –1 (√2x + 3) = 0

⇒ (√2x + 3) (2√2x – 1) = 0

⇒ x = – \(\frac{3}{\sqrt2}\) or x = \(\frac{1}{2\sqrt2}\)

⇒ x = – \(\frac{3}{\sqrt2}\)or x = \(\frac{1}{2\sqrt2}\) x \(\frac{\sqrt2}{\sqrt2}\) = \(\frac{\sqrt2}4\)