find the zeroes of quadratic polynomial 4 root 3x square + 5x - 2 root 3 and verify th - Maths - Polynomials

Question

find the zeroes of quadratic polynomial 4 root 3x square + 5x -
2 root 3 and verify th relationship between the zeroes and its
coefficients

Priyanka Kedia · Accepted Answer

$P (x) = 4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3} = 4 \sqrt{3} x^{2} + 8 x - 3 x - 2 \sqrt{3} = 4 x (\sqrt{3} x + 2) - \sqrt{3} (\sqrt{3} x + 2) = (\sqrt{3} x + 2) (4 x - \sqrt{3}) \Rightarrow P (x) = (\sqrt{3} x + 2) (4 x - \sqrt{3})$

If P(x) = 0,

$(\sqrt{3} x + 2) (4 x - \sqrt{3}) = 0 \Rightarrow x = - \frac{2}{\sqrt{3}} o r x = \frac{\sqrt{3}}{4}$

$T h e r e f o r e x = - \frac{2}{\sqrt{3}} a n d x = \frac{\sqrt{3}}{4} a r e z e r o s o f t h e P (x) .$

Now,

$S u m o f t h e z e r o s = (- \frac{2}{\sqrt{3}} + \frac{\sqrt{3}}{4}) = - \frac{5}{4 \sqrt{3}} = - \frac{C o e f f i c i e n t o f x}{C o e f f i c i e n t o f x^{2}}$

and,

$\Pr o d u c t o f t h e z e r o s = (- \frac{2}{\sqrt{3}} \times \frac{\sqrt{3}}{4}) = - \frac{1}{2} = \frac{C o n s \tan t t e r m}{C o e f f i c i e n t o f x^{2}}$

find the zeroes of quadratic polynomial 4 root 3x square + 5x - 2 root 3 and verify th relationship between the zeroes and its coefficients