If $(a − b) $,$ a$ and $(a + b)$ are zeros of the polynomial $2 x^{3} - 6 x^{2} + 5 x - 7$ , write the value of $a$.

Open in App

Solution

Given: $(a - b)$ , $a$ and $(a + b)$ are zeros of the polynomial $2 x^{3} - 6 x^{2} + 5 x - 7$
By using the relationship between the zeroes of the cubic polynomial.
We have,
$S u m o f z e r o e s = \frac{- c o e f f i c i e n t o f x^{2}}{c o e f f i c e n t o f x^{3}}$
$\Rightarrow a - b + a + a + b = \frac{- (- 6)}{2}$
$\Rightarrow 3 a = 3$
$\Rightarrow a = 1$
Hence, the value of $a$ is $1$

Suggest Corrections

Similar questions

If $(a - b), a a n d (a + b)$ are zeros of the polynomial $2 x^{3} - 6 x^{2} + 5 x - 7$ , write the value of a.

f (x) = 6 x^{2} + x - 2

\frac{a}{b} + \frac{b}{a}

f (x) = x^{2} - 5 x + k

If 9 and -5 are zeroes of the polynomial $x^{2} + (a + 5) x - b$ , then find the value of a and b. [2 MARKS]

f (x) = 2 x^{3} - 5 x^{2} + a x + b

Join BYJU'S Learning Program