Question

Find sum and product of roots of the quadratic equation x^2-4th root 3*x+9=0

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• A polynomial
• X²-4√3x+9

${\sf{\green{\underline{\large{To\:Find}}}}}$

• Factors of the polynomial

${\sf{\pink{\underline{\Large{Explanation}}}}}$

• X²-4√3x+9

• we have to spilt the middle term in such a way that the product become 9 and sum become -4√3

=>X²-4√3x+9

=>X²-3√3x-√3x+9

=>x(x-3√3)-√3(x-3√3)

=>(x-3√3)(X-√3)

=>X=3√3,√3

Additional Information

Let the zeroes of the polynomial be$\tt\alpha{and}\beta$

Then,

$\rightarrow\tt\alpha{+}\beta{=}3\sqrt{3}+{\sqrt{3}}=4{\sqrt{3}}$

&

$\rightarrow\tt\alpha{\times}\beta{=}9$

Here,

a=1

b=-4√3

C=9

☞

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{-4{\sqrt{3}}}{1}$

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{Cofficient\:of\:X}{Cofficient\:of\:x^2}=$

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{9}{1}$

$\rightarrow\tt{\large\alpha{\times}\beta{=}\dfrac{Constant\:term}{Cofficient\:of\:x^2}}$

Hence,relation verified