Find a quadratic polynomial, whose zeroes
are -2 and 3.
Answers
Answer :
The quadratic polynomial is x² - x - 6
Step-by-step explanation :
Given zeroes are -2 and 3,
we know,
The quadratic polynomial is of the form :
⇝ x² - (sum of zeroes)x + (product of zeroes)
x² - (-2 + 3) + [(-2)(3)]
x² - (1)x + (-6)
x² - x - 6
The required quadratic polynomial is x² - x - 6
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About 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
________________________________
Answer:
Answer :
The quadratic polynomial is x² - x - 6
Step-by-step explanation :
Given zeroes are -2 and 3,
we know,
The quadratic polynomial is of the form :
⇝ x² - (sum of zeroes)x + (product of zeroes)
x² - (-2 + 3) + [(-2)(3)]
x² - (1)x + (-6)
x² - x - 6
The required quadratic polynomial is x² - x - 6
--------------------------------------------
About 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
________________________________