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(37) Find the zeroes of the quadratic polynomial f(x) = 473x2 - 2 V3x - 2 v3 and verify the relationship between the zeros and the coefficients. |
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Answer» ong>Answer: FIRSTLY factorise the given POLYNOMIAL and then put each factor equal to zero to find required zeroes and then for verification show that
Sum of zeroes = - coefficient of x/coefficient of x² Product of zeroes = constant term/coefficient of x²
SOLUTION: 4√3x² +8X -3x -2√3
[By splitting the middle term] 4x (√3x +2) - √3(√3x +2) (4x-√3) (√3x +2)
To find zeros, put p(x)= 0 (4x-√3)= 0 or (√3x +2)= 0 4x = √3 or √3x = -2 x= √3/4 or x = -2/√3
Hence, zeroes of the polynomial are √3/4 and -2/√3.
Verification: Sum of zeroes = (√3/4) +(-2/√3) - coefficient of x/coefficient of x² =√3/4 -2/√3 - 5/4√3 = (√3×√3)-(2×4)/4√3 -5/4√3 =(3-8)/4√3 - 5/4√3 =-5/4√3
Product of zeroes = (√3/4) (-2/√3)= -½ constant term/coefficient of x² = -½ -2√3/ 4√3 = -½ -½ = -½
So, the relationship between the zeroes and its coefficients is verified. Step-by-step explanation:
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