The quantity b² - 4ac is called it's discriminant. The value of m should be less than -25/8.
Let the quadratic equation given be of the form ax² + bx + c = 0, then
The quantity b² - 4ac is called it's discriminant.
The solution contains the term \sqrt{b^2 - 4ac} which will be:
There are two roots of quadratic equations always(assuming the existence of complex numbers). We say that the considered quadratic equation has 2 solutions if roots are distinct, and has 1 solution when both roots are the same.
For the given quadratic equation, the graph will not touch the x-axis only if the roots of the quadratic equation are imaginary.
The roots of a quadratic equation are imaginary if the discriminant of the given equation is less than zero. Therefore, we can write the condition as,
D < 0
b² - 4ac < 0
(-5)² - 4(m)(-2) < 0
25 + 8m < 0
8m < -25
m < -25/8
Hence, the value of m should be less than -25/8.
Learn more about the Discriminant of a quadratic equation:
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