find zeroes and verify the relationship between zeroes and coofficent. 5x^2-14x+8
Answers
➢ Answer :
Zeroes of the polynomial p(x) = 2 & 4/5
➢ Given :
Polynomial p(x) = 5x² - 14x + 8
➢ To Find :
The zeroes of the polynomial p(x) and verify the relationship between zeroes and coefficients.
➢ How To Find :
p(x) = 5x² - 14x + 8
Now, 5x² - 14x + 8 = 0
By splitting the middle term, we get,
⇝ 5x² - 4x - 10x + 8 = 0
⇝ x(5x - 4) -2(5x - 4) = 0
⇝ (x - 2)(5x - 4) = 0
⇝ x = 2, 4/5
Therefore, zeroes of the polynomial p(x) = 2 and 4/5.
i.e., ɑ = 2 & β = 4/5
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➢ Verification :
If ɑ and β are the zeroes of the quadratic polynomial p(x) = ax² + bx + c, a ≠ 0, then
- ɑ + β = -b/a
- ɑ × β = c/a
Now, ɑ + β = 2 + 4/5 = 14/5
ɑ × β = 2 × 4/5 = 8/5
∴ ɑ + β = -b/a = -(-14)/5 = 14/5
ɑ × β = c/a = 8/5
Hence, the relationship between zeroes and coefficients are verified.
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Step-by-step explanation: