Question

Solution of a quadratic equation X²+5×-6=0

Answer 1

✪AnSwEr

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

• A polynomial
• X²+5x-6=0

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

• Factors of the polynomial
• Relationship between cofficient

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

X²+5x-6=0

• we have to spilt the middle term in such a way that the product become -6 and sum become 5x

X²+5x-6=0

=>X²+5x-6=0

=>x²+6x-x-6=0

=>x(x+6)-1(x+6)

=>(x+6) (x-1)

=>x=1,-6

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=1

b=5

C=-6

☞

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{-5}{1}$

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

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{-6}{1}$

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

Hence,relation verified

Answer 2

Given :-

Correct Question should be

${x}^{2} + 5x + 6 = 0$

What to find out =Roots of the equation?

Solution :-

Factorise by splitting middle term

$x {}^{2} + 5x + 6 = 0 \\ \\ {x}^{2} + 3x + 2x + 6 = 0 \\ \\ x(x + 3) + 2(x + 3) = 0 \\ \\ (x + 3)(x + 2) = 0$

Now split it into possible cases

$(x + 3) = 0 \\ \\ (x + 2) = 0$

Hence,

$x_1 = (- 3) \\ \\ \\ x_2 = ( - 2)$

Extra information :-

• A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.