Plz help!! juzt 2 questionz!! thankz!!?

Question

Match the terms with the definitions.

Term

c2 + 10c - 25 = 0

a2 - 5a - 14 = 0

16y2 - 8y + 1 = 0

5x2 + 8x + 16 = 0

Definition

A) 1 real (rational)

B) 2 complex (conjugate)

C) 2 rational roots

D) 2 irrational roots

POINT VALUE: 4

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If a quadratic does not have a linear term (in other words it is a "pure quadratic"), then it will always have 2 real solutions.

True

False

Answer 1

For the first problem, we're concerned about the discriminant, which is b^2 - 4ac, if we have written the quadratic in form:

ax^2 + bx + c = 0

For the first one, the discriminant is 200, a positive number. This means we should have two real roots. We also know that 200 is not a perfect square. Knowing the quadratic formula, we know we'll have to take the square root of 200, which is inevitable leads to two irrational numbers. In case you're wondering, the answers are approximately 2.07 and -12.07.

In the second one, the discriminant is 81, a positive number so both roots are real. It is a also perfect square, so both roots are rational. The roots are 7 and -2.

In the third one, the discriminant is zero, so we have only one real root. It is 0.25.

By process of elimination, we can assume that the final one has two complex roots. By calculating the discriminant to be a negative number, our suspicion is confirmed. The discriminant is -256 and the roots are -0.8 +/- 1.6 i.

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False. Counterexample: x^2 + 4 = 0 has no real solutions.