Find the quadratic polynomial whose roots are -3 and 2 respectively
Answers
Answer :
x² + x - 6
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,
zeroes of the polynomial are -3 and 2
Sum of zeroes = -3+2
= -1
Product of zeroes = (-3) (2)
= -6
The quadratic polynomial is of the form,
x² - (sum of zeroes)x + (product of zeroes)
=> x² - (-1)x + (-6)
=> x² + x - 6
Step-by-step explanation:
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