Question

find the zeroes of the quadratic polynomial 6x²-7x -3 and verify the reaction between the zeroes and the conflicts ​

Answer 1

✪AnSwEr

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

• A polynomial
• 6x²-7x -3

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

• Factors of the polynomial
• Relationship between cofficient

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

6x²-7x -3

• we have to spilt the middle term in such a way that the product become -18 and sum become -7x

6x²-7x -3

=>6x²-9x+2x -3

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

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

=>x=3/2 , -1/3

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=-3

☞

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

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

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{-3}{6}$

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

Hence,relation verified

Answer 2

✯✯ QUESTION ✯✯

Find the Zeroes of the Quadratic Polynomial 6x²-7x -3 and Verify the Reaction between the Zeroes and the Conflicts ..

✰✰ ANSWER ✰✰

$\implies\tt{{6x}^{2}-7x-3}$

➥By Splitting Middle Term :

$\implies\tt{\bold{{6x}^{2}-(9x-2x)-3}}$

$\implies\tt{{6x}^{2}-9x+2x-3}$

$\implies\tt{3x(2x-3)+1(2x-3)}$

$\implies\tt{(3x+1)(2x-3)}$

• x = -1/3
• x = 3/2

Here : -

• a = 6
• b = -7
• c = -3

━━━━━━━━━━━━━━━━━━━━

★Sum Of Zeroes : -

$\implies\tt{\alpha+\beta=\dfrac{-b}{a}}$

$\implies\tt{\dfrac{-1}{3}+\dfrac{3}{2}=\dfrac{-(-7)}{6}}$

$\implies\tt{\dfrac{-2+9}{6}=\dfrac{7}{6}}$

$\implies\tt{\dfrac{7}{6}=\dfrac{7}{6}}$

$\green\longmapsto\:\large\underline{\boxed{\bf\pink{L.H.S}\red{=}\blue{R.H.S}}}$

★Product of Zeroes : -

$\implies\tt{\alpha\beta=\dfrac{c}{a}}$

$\implies\tt{\dfrac{-1}{3}\times\dfrac{3}{2}=\dfrac{-3}{6}}$

$\implies\tt{\cancel\dfrac{-3}{6}=\cancel\dfrac{-3}{6}}$

$\implies\tt{\dfrac{-1}{2}=\dfrac{-1}{2}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{L.H.S}\orange{=}\purple{R.H.S}}}$

✺ HENCE VERIFIED ✺