Question

6x^2 - root 5 x -2=0 find its roots

Answer 1

✪AnSwEr

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

• A polynomial
• 6X²+7X+2

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

• Factors of the polynomial
• Relationship between cofficient

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

6X²+7X+2

• we have to spilt the middle term in such a way that the product become 12 and sum become 7

6X²+7X+2

=>6X²+7X+2

=>6x²+4x+3x+2

=>2x(3x+2)+1(3x+2)

=>(3x+2)(2x+1)

Additional Information

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

Then,

$\rightarrow\tt\alpha{+}\beta{=}\frac{-b}{a}$

&

$\rightarrow\tt\alpha{\times}\beta{=}\frac{c}{a}$

Here,

a=6

b=7

C=2

☞

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{7}{6}$

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

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{2}{6}$

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

Hence,relation verified