check whether 0-1 and ¼ are zeroes of polynomial p(x)=4x²+3x-1
Answers
Correct Question :
Check whether -1 and ¼ are zeroes of polynomial p(x)=4x²+3x-1
Answer :
-1 and ¼ are zeroes of polynomial p(x)=4x²+3x-1
Step-by-step explanation :
➤ Quadratic Polynomials :
✯ 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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Given polynomial,
p(x) = 4x² + 3x - 1
we have to check whether -1 and 1/4 are the zeroes of the given polynomial.
- substitute x = -1,
p(-1) = 4(-1)² + 3(-1) - 1
= 4(1) - 3 - 1
= 4 - 3 - 1
= 4 - 4
= 0
Since p(-1) = 0,
∴ -1 is a zero of the polynomial 4x²+3x-1
- substitute x = 1/4
p(1/4) = 4(1/4)² + 3(1/4) - 1
= 4(1/16) + 3/4 - 1
= 1/4 + 3/4 - 1
= 4/4 - 1
= 1 - 1
= 0
Since p(1/4) = 0,
∴ 1/4 is a zero of the polynomial 4x²+3x-1