Question

Given the equation 2x2 - 5x + 7 = 0. Find the discriminant. Describe the roots and explain your reasoning.

Answer 1

The discriminant of a quadratic equation is a parameter that is used to determine the nature of the roots of the equation. The discriminant can be determined by b2- 4ac. In this case, upon substitution, 25- 4*2*7 = -31 in which the roots are negative and iimaginary. 

Answer 2

The negative value of the discriminant shows that there are no real roots of the quadratic equation.

What is the value of the discriminant?

The value of the discriminant tells which type of roots the quadratic equation will have. We know that the value of the discriminant is given as,

$D= b^2-4ac$

As we know that the values of the discriminant decide which type of roots the quadratic equation may have, therefore, if the value of the discriminant is negative the roots are imaginary if the value of the discriminant is zero then there is one real root, and if the value of the discriminant is positive then there are two real roots.

As given to us the quadratic equation 2x²-5x+7= 0, therefore, we can write the coefficient values as, a=2, b=-5, and c=7.

Now, We know the formula of the discriminant can be written as,

$D= b^2-4ac\\\\D = (-5)^2-4(2)(7)\\\\D = 25 -56\\\\D = -31$

Hence, the negative value of the discriminant shows that there are no real roots of the quadratic equation.

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