If x = 2 is a zero of the polynomial p(x) = 2x²+3x –n, then the value of 'n' is
Answers
Answer:
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Answer:
The required value of n is 14.
Step-by-step explanation:
Given :
x = 2 is a zero of the polynomial p(x) = 2x² + 3x – n
To find :
the value of n
Solution :
p(x) = 2x² + 3x – n
As 2 is a zero of the given polynomial, the result is zero when we substitute x = 2.
p(2) = 0
Put x = 2,
2(2)² + 3(2) – n = 0
2(4) + 6 – n = 0
8 + 6 – n = 0
14 – n = 0
n = 14
Therefore, the value of n is 14
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About Quadratic Polynomial :
✯ It is a polynomial of degree 2
✯ General form :
ax² + bx + c = 0
✯ Determinant, D = b² - 4ac
✯ Based on the value of Determinant, we can define the nature of roots.
D > 0 ; real and unequal roots
D = 0 ; real and equal roots
D < 0 ; no real roots i.e., imaginary
✯ Relationship between zeroes and coefficients :
✩ Sum of zeroes = -b/a
✩ Product of zeroes = c/a
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