Use the discriminant and select whether the roots of 5x2 - 4x + 3 = 0 are real or non-real.
Answer: The roots for the equation 5 x2 + 4x + 3 = 0 are non real since the value of the discriminant D = -44 < 0.
Let's find the value of discriminant and nature of roots.
A discriminant of a quadratic equation is a function of the coefficients of the polynomials.
To find the nature of roots of a quadratic equation we will use the discriminant.
The discriminant is given by D = b2 - 4 ac
- If D > 0, the equation has two real and distinct roots
- If D = 0, the equation has real and equal roots.
- If D < 0, the equation has no real roots or complex roots.
Where a = coefficient of x2, b = coefficient of x and c = constant term.
Now, consider the given equation 5x2 - 4x + 3 = 0
a = 5, b = -4, c = 3
Let's check for the discriminant b2 - 4 ca as shown below
⇒ ( - 4 ) 2 - 4 × ( 5 ) × ( 3 )
⇒ 16 - 4 × ( 15)
⇒ 16 - ( 60 )
⇒ - 44 < 0 → The equation has no real roots.