Question

6x sp +17x+5 solve this by splitting middle term​

Answer 1

Given :-

$6 {x}^{2} + 17x + 5 = 0$

What to find out =Roots of the equation?

Solution :-

Factorise by splitting middle term

$6 {x}^{2} + 17x + 5 = 0 \\ \\ 6 {x}^{2} + 15x + 2x + 5 = 0 \\ \\ 3x(2x + 5) + 1(2x + 5) = 0 \\ \\ (2x + 5)(3x + 1) = 0$

Now split it into possible cases

$(2x + 5) = 0 \\ \\ (3x + 1) = 0$

Hence,

$x_1 = ( - \frac{5}{2} )\\ \\ \\ x_2 = ( - \frac{ 1}{3} )$

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.

Answer 2

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Question}}}}}}}}$

$\sf 6x^2 + 17x + 5$

solve this by mid term split

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Solution}}}}}}}}$

$\sf\implies 6x^2 + 17x + 5$

$\sf\implies 6x^2 + 15x + 2x + 5$

$\sf\implies 3x(2x + 5)+1(2x+5)$

$\sf\implies(3x+1)(2x+5)$

• roots in the equation

$\sf\implies 3x+1 = 0$

$\sf\implies 3x= - 1$

$\sf\implies x =\dfrac{-1}{3}$

_________________

$\sf\implies 2x+5 = 0$

$\sf\implies 2x= - 5$

$\sf\implies x =\dfrac{-5}{2}$

${\bold{\blue{\boxed{\bf{\dfrac{-1}{3}}}}}}$ And ${\bold{\blue{\boxed{\bf{\dfrac{-5}{2}}}}}}$

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THANK YOU ❤