The zeros of the polynomial 7x2 - \(\frac{11}{13}\)x - \(\frac{2}{3}

1.	The zeros of the polynomial 7x2 - \(\frac{11}{13}\)x - \(\frac{2}{3}\) are(a) \(\frac{2}{3}\), \(\frac{-1}{7}\)(b) \(\frac{2}{3}\), \(\frac{-1}{3}\)(c) \(\frac{-2}{3}\),\(\frac{1}{7}\)(d) none of these
Answer» (a) \(\frac{2}{3}\), \(\frac{-1}{7}\) Let f(x) = 7x² – \(\frac{11}3\) x – \(\frac{2}3\) = 0 ⇒21x² – 11x – 2 = 0 ⇒21x² – 14x + 3x – 2 = 0 ⇒7x (3x – 2) + 1(3x – 2) = 0 ⇒ (3x – 2) (7x + 1) = 0 ⇒ x = \(\frac{2}3\) or x = \(\frac{-1}7\)

The zeros of the polynomial 7x2 - \(\frac{11}{13}\)x - \(\frac{2}{3}\) are(a) \(\frac{2}{3}\), \(\frac{-1}{7}\)(b) \(\frac{2}{3}\), \(\frac{-1}{3}\)(c) \(\frac{-2}{3}\),\(\frac{1}{7}\)(d) none of these

Answer»

(a) \(\frac{2}{3}\), \(\frac{-1}{7}\)

Let f(x) = 7x² – \(\frac{11}3\) x – \(\frac{2}3\) = 0

⇒21x² – 11x – 2 = 0

⇒21x² – 14x + 3x – 2 = 0

⇒7x (3x – 2) + 1(3x – 2) = 0

⇒ (3x – 2) (7x + 1) = 0

⇒ x = \(\frac{2}3\) or x = \(\frac{-1}7\)