Find the zeros of quadratic polynomial √3x²- 5x + √3 and verify the relationship between zeros and the
coefficients.
Answers
Find the zeros of the polynomial f(x) =4√3x²+5x-2√3 verify the relationship between the zeros & its coefficients?
The given polynomial f(x)
= 4√3 x^2 +5x - 2√3
= 4√3 x^2 + 8x - 3x - 2√3
= 4x(√3 x +2) - √3 (√3 x +2)
= (√3x+2)(4x-√3)
Hence the zeroes are -2/√3 and √3/4
Sum of the roots = -2/√3 + √3/4 = -2√3/3 + √3/4 = (-8√3+3√3)/12 = -5√3/12
Sum of the roots = -b/a = -5/4√3 = -5√3/12
Hence sum of the roots =-b/a.
Product of the roots = (-2/√3)(√3/4) = -1/2.
Product of the roots = c/a = -2√3/4√3 = -1/2.
So product of the roots = c/a.
Thus, the relationship between the roots and coefficients is verified.
Answer:
The given polynomial f(x)
= 4√3 x^2 +5x - 2√3
= 4√3 x^2 + 8x - 3x - 2√3
= 4x(√3 x +2) - √3 (√3 x +2)
= (√3x+2)(4x-√3)
Hence the zeroes are -2/√3 and √3/4
Sum of the roots = -2/√3 + √3/4 = -2√3/3 + √3/4 = (-8√3+3√3)/12 = -5√3/12
Sum of the roots = -b/a = -5/4√3 = -5√3/12
Hence sum of the roots =-b/a.
Product of the roots = (-2/√3)(√3/4) = -1/2.
Product of the roots = c/a = -2√3/4√3 = -1/2.
So product of the roots = c/a.
Step-by-step explanation:
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