The value of b²- 4ac for the quadratic equation x² + 5x + 4 = 0 is 9.
What is the discriminant of a polynomial?
The discriminant of a polynomial is a function of its coefficients and is represented by the capital ‘D’ or Delta symbol (Δ). It shows the nature of the roots of any quadratic equations where a, b, and c are real numbers.
It is represented as ‘D’
D = b² - 4ac
Where,
a is the coefficient of x²,
b is the coefficient of x,
c is a constant term.
The nature of roots is based on the value of the discriminant:
D > 0; the quadratic equation has real and distinct roots
D = 0; the quadratic equation has real and equal roots
D < 0; the quadratic equation has complex roots
We have given,
The quadratic equation : x² + 5x + 4 = 0
For the quadratic equation of the form ax² + bx + c, the value of the discriminant is given by
D = b² – 4ac
For the given Quadratic equation,
a = 1
b = 5
c = 4
Discriminant, D = (5)² – 4(1)(4)
D = 25 - 16
D = 9
D > 0,
so, the quadratic equation has real and distinct roots
Hence, the value of b²- 4ac for the quadratic equation x² + 5x + 4 = 0 is 9.
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