1.) Find the value of the discriminant and the the number of real solutions of x^2-8x+7=02.) Find the value of the discriminant and the number of real solutions of2x^2+4x+2=0

Hi there!

When we have an equation standard form...
[tex]a {x}^{2} + bx + c = 0[/tex]
...the formula of the discriminant is
D = b^2 - 4ac

When
D > 0 we have two real solutions
D = 0 we have one real solutions
D < 0 we don't have real solutions

1.) Find the value of the discriminant and the the number of real solutions of
x^2-8x+7=0

Plug in the values from the equation into the formula of the discriminant

[tex]( - 8) {}^{2} - 4 \times 1 \times 7 = 64 - 28 = 36[/tex]

D > 0 and therefore we have two real solutions.

2.) Find the value of the discriminant and the number of real solutions of
2x^2+4x+2=0

Again, plug in the values from the equation into the formula of the discriminant.

[tex] {4}^{2} - 4 \times 2 \times 2 = 16 - 16 = 0[/tex]

D = 0 and therefore we have one real solution.

~ Hope this helps you.