If a and B are the zeroes of quadratic polynomial such that a + B = 24 and a - B = 8. find the quadratic polynomial having a and B as its zeroes. Verify the relationship between the zeroes and coefficients of the polynomial
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Quadratic equation = x² - 24x + 128
Step-by-step explanation:
For quadratic equation
k((x² -(sum of roots)x + (product of roots))
Sum of roots = a + b = 24(Given)
Product of roots = a*b
a+b = 24 (Elimination used to solve the pair of linear equation) -----(1)
a-b = 8 ------(2)
- +. -
0+2b = 16
2b = 16
b = 16/2
b = 8
Applying value of b in equation (2)
a-b = 8
a-8 = 8
a = 8+8
a = 16
Product of roots = a*b
= 16*8
= 128
Quadratic equation = x² - 24x + 128
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