Question

Find the product of roots of a quadratic equation 2x^2 +7x- 4 = 0​

Answer 1

GIVEN :-

• A quadratic equations 2x² + 7x - 4.

TO FIND :-

• The roots of the quadratic equation.

SOLUTION :-

$\implies \displaystyle \sf \: 2x ^{2} + 7x - 4 = 0$

$\implies \displaystyle \sf \:2x ^{2} - 8x + x - 4 = 0$

$\implies \displaystyle \sf \:2x(x - 4) + 1(x - 4) = 0$

$\implies \displaystyle \sf \:(x - 4)(2x + 1) = 0$

$\implies \displaystyle \sf \:x - 4 = 0 \: or \: 2x + 1 = 0$

$\implies \displaystyle \sf \:x = 0 + 4 \: or \: 2x = - 1$

$\implies \displaystyle \sf \:x = 4 \: or \: x = \frac{ - 1}{2}$

Therefore roots of the given equation are either 4 or -1/2 .

Now we have to find the product of roots,

$\implies \displaystyle \sf \:product \: = 4 \times \frac{ - 1}{2}$

$\implies \displaystyle \sf \:product \: = \frac{ - 4}{2}$

$\implies \underline{ \boxed{ \pink{\displaystyle \sf \:product \: = - 2}}}$

Answer 2

Given :-

$\sf 2x^2 + 7x -4=0$

Solution :-

$\sf 2x^2 + (8x-x)-4=0$

$\sf 2x^2 - 8x+x-4=0$

$\sf 2x(x-4)+1(x-4)=0$

$\sf (x-4)(2x+1)=0$

So,

$\sf x = 0+4$

$\sf x = 4$

or

$\sf x = \dfrac{-1}{2}$

we know that

Product = 4 × -1/2

Product = -4/2

Product = -2