If the value of the polynomial x2-6 x-8 at x-a is -1- then what is the value of a -

The correct option is D 3The given polynomial is f(x) = x2 − 6x + 8. It is given that f(a) = −1. At x = a, f(a) = a2 − 6a + 8. ∴f(a) = −1 ⇒ a2 − 6a + 8 = −1 ⇒ ...

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Standard IX

Mathematics

Polynomial Expressions

If the value ...

Question

If the value of the polynomial x²− 6x + 8 at x = a is −1, then what is the value of a?

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Solution

The correct option is D
3

The given polynomial is f(x) = x² − 6x + 8.

It is given that f(a) = −1.

At x = a, f(a) = a² − 6a + 8.

∴f(a) = −1

⇒ a² − 6a + 8 = −1

⇒ a² − 6a + 8 + 1 = 0

⇒ a² − 6a + 9 = 0

⇒ a² − 2 ×a × 3+ 3² = 0

⇒ (a − 3)² = 0 [a² − 2ab + b² = (a − b)²]

⇒ a − 3 = 0

⇒ a = 3

Thus, the value of a is 3.

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If the value of the polynomial x2 − 6x + 8 at x = a is −1, then what is the value of a?

If the value of the polynomial x²− 6x + 8 at x = a is −1, then what is the value of a?