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.

Open in App

Solution

$f (x) = 2 x^{3} - 6 x^{2} + 5 x - 7$

Let $α, β a n d γ$ be the zeroes.

Then, $α = a - b, β = a a n d γ = a + b$

We know that if $α, β a n d γ$ are the zeroes of a cubic polynomial,

$a x^{3} + b x^{2} + c x + d = 0$

$t h e n, α + β + γ = \frac{- b}{a}$

$(a - b) + a + (a + b) = \frac{- (- 6)}{2}$

$3 a = 3$

$a = 1$

So, the value of $a = 1$

Suggest Corrections

Similar questions

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

If $a, a + b, a + 2 b$ are zeroes of the cubic polynomial $x^{3} - 6 x^{2} + 3 x + 10$ , then $a + b =$ ________.

Join BYJU'S Learning Program