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In this lesson, we will learn how to find the discriminant of a quadratic equation and use it to determine the number and type of its roots (solution) without solving it.

Q1:

How many non-real roots will a quadratic equation have if its discriminant is positive?

Q2:

How many non-real roots will a quadratic equation have if its discriminant is negative?

Q3:

Determine the type of the roots of the equation 4 π₯ ( π₯ + 5 ) = β 2 5 .

Q4:

Determine whether the roots of the equation π₯ + π₯ β 2 = 0 2 are rational or not without solving it.

Q5:

Which is the correct condition for the quadratic equation π π₯ + π π₯ + π = 0 2 with real coefficients to have no nonreal roots?

Q6:

The roots of the equation 3 π₯ β ( 4 π β 9 ) π₯ + π β 1 = 0 ο¨ have different signs. Find the interval in which π lies.

Q7:

If the roots of the equation 2 4 π₯ + 6 π₯ + π = 0 2 are not real, find the interval which contains π .

Q8:

How many real roots does the equation π π₯ + π π₯ + π = 0 2 have if π β 0 and π β 4 π π = 0 2 ?

Q9:

Determine the type of the roots of the equation ( π₯ β 9 ) β π₯ ( π₯ β 5 ) = 0 .

Q10:

Which of the following describes the roots of the equation ?

Q11:

How many real roots does the following equation have?

Q12:

If the roots of the equation 2 π₯ + 1 0 π₯ + 1 2 + 1 π = 0 2 are equal, what is the value of π ?

Q13:

Are the roots of the equation π₯ + 6 π π₯ + 6 π = 1 2 rational for all rational values of π ?

Q14:

Given that the roots of the equation β 1 8 π₯ + 3 π π₯ β 7 2 = 0 ο¨ are equal, determine all possible values of π . For each value of π , work out the roots of the equation.

Q15:

Given that π is a real number, and the equation ( 4 π + 8 ) π₯ β 4 π π₯ + π = 0 2 does not have real roots, find the interval which contains π .

Q16:

If the roots of the equation π₯ β 8 ( π + 1 ) π₯ + 6 4 = 0 2 are equal, find the possible values of π .

Q17:

If the roots of the equation 4 π₯ β π π₯ + 1 = 0 2 are equal, what are the possible values of π ?

Q18:

Given that the equation π₯ β ( β 2 π + 2 8 ) π₯ + π = 0 2 2 has no real roots, find the interval that contains π .

Q19:

What type of roots does the equation 6 π₯ + π π₯ + π β 1 1 = 0 2 have for all real values of π ?

Q20:

Determine the type of the roots of the equation β 2 π₯ β 6 = 8 π₯ + 7 .

Q21:

Determine the type of the roots of the equation π₯ + 3 6 π₯ = 1 2 .

Q22:

Does the equation π₯ + 2 π π₯ + π = 9 π + 8 π 2 2 2 2 have real roots for all real values of π , π , and π ?

Q23:

Suppose the two roots of the equation π₯ β ( π + 6 ) π₯ β ( 1 0 π β 9 ) = 0 ο¨ are equal. Determine all possible values of π , and then find the two roots.

Q24:

Given that π and π are rational, non zero numbers, are the roots of the equation β π π₯ β 3 οΉ π β π ο π₯ + 9 π π = 0 2 2 2 2 always rational?

Q25:

If the roots of the equation π₯ β π π₯ β 4 π β 4 π₯ + 4 = 0 2 are equal, what are the possible values of π ? For each value of π , work out the roots of the equation.

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