Question

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 1

(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 \(\frac{\sqrt2}{\sqrt2}\) = \(\frac{\sqrt2}4\)