ind the zeroes of a quadratic polynomial 4√3 2 + 5x - 2√3 also verify the relationship between zeroes and coefficients.
Answers
Answer:
Hence, zeroes of the polynomial are √3/4 and -2/√3. So, the relationship between the zeroes and its coefficients is verified
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:
Let p(x) = 4√3x² +5x -2√3
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.
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