12.5 The quadratic formula — Practise

1. Solve $x^2-5x+2=0$ using the quadratic formula.

Answer: $x=(5+\sqrt{17})/2$ or $x=(5-\sqrt{17})/2$.

2. Solve $2x^2+3x-2=0$ using the quadratic formula.

Answer: $x=1/2$ or $x=-2$.

3. State the number of real roots of $x^2+2x-3=0$.

Answer: Two real roots because the discriminant is positive.

4. State the number of real roots of $x^2-6x+9=0$.

Answer: One repeated real root because the discriminant is zero.

5. State the number of real roots of $x^2+1=0$.

Answer: No real roots because the discriminant is negative.

6. Solve $3x^2-2x-1=0$ using the quadratic formula.

Answer: $x=1$ or $x=-1/3$.

7. Solve $x^2+4x-1=0$ using the quadratic formula.

Answer: $x=-2+\sqrt5$ or $x=-2-\sqrt5$.

8. Find the discriminant of $2x^2-4x+5=0$ and state the number of real roots.

Answer: The discriminant is $-24$, so there are no real roots.