Question

Find the discriminant and determine the nature of the roots to the quadratic equation

Answer 1

№17

`x^(2) +6x-7=0 \\ D=6 ^(2) -4*(-7)=36+28=64=8 ^(2) \\ \\ x_(1) = (-6+8)/(2) =1 \\ \\ x_(2) = (-6-8)/(2) =-7`
Answer: x₁ = 1
x₂ = - 7

№18

`2 x^(2) -3x+4=3 \\ 2 x^(2) -3x+4-3=0 \\ 2 x^(2) -3x+1=0 \\ \\ D= -3 ^(2) -4*2=9-8=1 \\ \\ x_(1) = (3+1)/(2*2) = (4)/(4) =1 \\ \\ x_(2) = (3-1)/(2*2) = (2)/(4) =0.5`
Answer: x₁ = 1
x₂ = 0,5.

№19

`2 x^(2) -4x-5=0 \\ D=-4 ^(2) -4*2*(-5)=16+40=56 \\ \\ x_(1)= (4+ √(56) )/(2*2) = (4)/(4) + \sqrt{ (56)/(16) } =1+ √(3.5) \\ \\ x_(2) = (4- √(56) )/(2*2) = (4)/(4) - \sqrt{ (56)/(16) } =1- √(3.5)`
Answer: x₁ = 1 + √3.5
x₂ = 1 - √3.5