9. If the sum of zeroes of the quadratic polynomial 3x2 - kx
+ 6 is 3, then find the value of k.
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Answer :
k = 9
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
________________________________
Given polynomial,
3x² - kx + 6
It is of the form ax² + bx + c
a = 3 , b = -k , c = 6
Sum of the zeroes = 3
-b/a = 3
-(-k)/3 = 3
k/3 = 3
k = 3 ×3
k = 9
The value of k is 9
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