f4 maths discriminant help>

In fact, part a and part b are related. Putting y = 0 to find the determinant

The determinant

a. < 0, means that the number of x-intercept is zero. (no real root)

b. = 0, means that the number of x-intercept is one. (double root)

c. > 0, means that the numbers of x-intercept are two. (distinct real roots)

(P.S. For a quadratic equation ax^2 + bx + c = 0, determinant = b^2 - 4ac)


1.a. y = x^2 - 9x + 4

Put y = 0, x^2 - 9x + 4 = 0

Determinant = (-9)^2 - 4(1)(4) = 65 > 0

So, the numbers of x-intercept of the graph are 2.

b. y = 8x^2 + 8x + 2

Put y = 0, 8x^2 + 8x + 2 = 0

Determinant = (8)^2 - 4(8)(2) = 0

So, the number of x-intercept of the graph is 1.

c. y = -5x^2 + 3x - 1

Put y = 0, -5x^2 + 3x - 1 = 0

Determinant = (3)^2 - 4(-5)(-1) = -11 < 0

So, the number of x-intercept of the graph is 0.