Question

Different types of question from polynomial class 10.
If zero of a polynomial (a2-9)X2+13X+6a is a reciprocal of other, find value of a

Answer 1

Hi mate your answer is ⤵⤵⤵⤵⤵⤵
❄Question:-If one zero of the polynomial (α2 + 9) x2 + 13x + 6α is reciprocal of the other, find the value of a.

❄Answer :
Let one zero of the given polynomial is
$\alpha$

According to the given condition,
The other zero of the polynomial is
$1 \div \alpha$

We have,
Product of zeroes,
$\alpha \beta = c \div a$
$= 6 \alpha \div \alpha {}^{2} + 9$
$\alpha \times 1 \div \alpha = 6 \alpha \div \alpha {}^{2} + 9$


⇒ α2 – 6α + 9 = 0
⇒ α2 – 3α – 3α + 9 = 0
⇒ α(α – 3) – 3(α – 3) = 0
⇒(α – 3)(α – 3) = 0
⇒(α – 3) = 0 & (α – 3) = 0
⇒ α = 3, 3
Hope it helps you.
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