Find the discriminant of the following quadratic equationsand describe the roots.a. x2-5x+4=0b. x2-8x+16=0c. 2x²+x-2=0d. 3x²+3x+1=0​

[tex]Let's calculate the discriminant for each quadratic equation and describe the roots:a. For the equation \( x^2 - 5x + 4 = 0 \):- \( a = 1 \)- \( b = -5 \)- \( c = 4 \)The discriminant is calculated as:\[(-5)^2 - 4(1)(4) = 25 - 16 = 9\]Since the discriminant is 9 (positive), the equation has two distinct real roots.---b. For the equation \( x^2 - 8x + 16 = 0 \):- \( a = 1 \)- \( b = -8 \)- \( c = 16 \)[/tex][tex]The discriminant is:\[(-8)^2 - 4(1)(16) = 64 - 64 = 0\][/tex]Since the discriminant is 0, the equation has exactly one real root (a repeated root).[tex]---c. For the equation \( 2x^2 + x - 2 = 0 \):- \( a = 2 \)- \( b = 1 \)- \( c = -2 \)The discriminant is:\[1^2 - 4(2)(-2) = 1 + 16 = 17\]Since the discriminant is 17 (positive), the equation has two distinct real roots.---d. For the equation \( 3x^2 + 3x + 1 = 0 \):- \( a = 3 \)- \( b = 3 \)- \( c = 1 \)The discriminant is:\[3^2 - 4(3)(1) = 9 - 12 = -3\]Since the discriminant is -3 (negative), the equation has two complex roots.[/tex]

Answered by VeniceSangolan | 2024-09-04