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In this lesson, we will learn how to solve quadratic equations using the quadratic formula.

Q1:

Solve the equation β π₯ + 7 π₯ + 1 = 0 2 .

Q2:

Find the solution set of the equation 3 π₯ β 2 ( 7 β π₯ ) = 0 2 , giving values to one decimal place.

Q3:

Find the solution set of the equation π₯ β 8 π₯ β 2 = 9 π₯ + 8 2 , giving values correct to three decimal places.

Q4:

Find the solution set of the equation 5 π₯ β 7 π₯ β 3 2 = 0 2 , giving values to three decimal places.

Q5:

Find the solution set of the equation 1 8 π₯ + 5 π₯ = 1 2 , giving values to three decimal places.

Q6:

Find the solution set of 1 6 π§ = 3 2 π§ β 1 5 2 in β .

Q7:

Find the solution set of the equation 5 π₯ ( π₯ β 6 ) β 3 ( π₯ + 4 ) + 3 = 0 , giving values to one decimal place.

Q8:

Find the solution set of the equation 2 π₯ β 5 = 6 π₯ , giving values to three decimal places.

Q9:

Given that π₯ = β 1 is one of the roots of the equation β 3 π₯ β 9 π₯ + π = 0 2 , find the other root and the value of π .

Q10:

Find the solution set of the equation ( π₯ β 5 ) β ( π₯ β 5 ) β 3 = 0 2 , giving values to one decimal place.

Q11:

The sum of the roots of the equation 4 π₯ + π π₯ β 4 = 0 2 is β 1 . Find the value of π and the solution set of the equation.

Q12:

Given that is a root of the equation , find the set of possible values of ?

Q13:

Find the solution set of the equation 3 π₯ + 3 β 4 π₯ β 3 = 3 in β , giving values to one decimal place.

Q14:

The dimensions of a rectangle are 5 m and 12 m. When both dimensions are increased by a given amount, the area of the rectangle will double. What is the amount?

Q15:

Find the solution set of the equation in , giving values to one decimal place if necessary.

Q16:

If πΏ and π are the roots of the equation π₯ + 2 4 π₯ β 6 = 0 2 , what is the value of πΏ + 2 4 πΏ β 1 7 2 ?

Q17:

Find the solution set of π₯ + 1 7 π₯ = 6 in β , giving values to one decimal place.

Q18:

By using the quadratic formula, solve the equation 2 π₯ + 3 π₯ = 7 2 . Give your answers correct to two decimal places.

Q19:

Use the quadratic formula to find all the values of π for which the roots of the equation 2 π₯ + π π₯ β 7 = 0 2 differ by exactly 10. Give your answers correct to two decimal places if necessary.

Q20:

Find the solution set of the equation ( π₯ β 2 3 ) β 6 π₯ = 0 2 , giving values to three decimal places.

Q21:

Find the solution set in β of the equation 4 π₯ β 2 π₯ = 1 , giving values to one decimal place.

Q22:

Using the quadratic formula, find all the solutions to π₯ β 1 0 π₯ + 1 = 0 4 2 .

Q23:

Find the solution set of the equation π₯ + 4 6 π₯ = 2 2 , giving values to three decimal places.

Q24:

Find the solution set of π₯ β 6 ( π₯ β 1 ) = 2 2 in β , giving values to two decimal places.

Q25:

Find the solution set of the equation , giving values to three decimal places if necessary.

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