Given that x² + 8x +Q = (x + K)². Find the value of K and Q

Solve the equation x²-10x +13=0 by completing the square. Leave the answer in surd form

Find two consecutive positive numbers such that the sum of their squares is equal to 145.

(b) The sum of square of two consecutive positive number is 61. Find the numbers.

The sum of square of two consecutive positive number is 61. Find the numbers.

Rachel is three years older than her brother John. Three years to come, the product of their ages will be 130 years. Formulate a quadratic equation representing this information. Hence, by using the quadratic formula, find their present ages.

10. Find two positive numbers whose difference is 5 and whose product is 266.

Solve the equation 2x² + 3x - 5=0 by completing the square

Solve the equation 2x² + 3x - 5=0 by completing the square

Solve the equation 2x² + 3x - 5=0 by completing the square

.Use the figure below to answer the following questions:

 (i). Write the expression for the total area of rectangles A and B.

    (ii). If the total area of rectangles A and B is 98 square centimeters, find the value of x

Use factorization method to solve the quadratic equation x² ? 9x + 14 = 0.

   Find the values of x that satisfies the equation 

  Anna is 6 years younger than her brother Jerry. If the product of their ages is 135, find how old is Anna and Jerry.

Solve the equation 4x² - 32x + 12 = 0 by using the quadratic formula.

10.If ²−²=10 and +=2, find the value of − 

If one of the roots of the quadratic equation x² + bx + 24 = 0 is 1¹₂ , find the value of b.

Two numbers differ by 3. If the sum of their reciprocals is  , find the numbers.

Solve the equation 

Solve the quadratic equation x² + 7x +12 = 0 by using the factorization method.

Solve the quadratic equation x² – 8x +7 = 0

A field is 10m longer than its wide. The area is 7,200m². What is the width?

Given that x² –y² = 27 and x + y = 9 find the value of xy

Solve the equation 2x² – 3x – 5 = 0 by completing the square.

A trapezium has the area of 2x² - 8x+6 square units. If the parallel sides are (2x+3) units and (2x - 7) units long, find its height.

The difference between two positive numbers is 7. If their product is 30, find the numbers.

A garden measuring 12 by 16 metres is to have a pedestrian pathway of equal width constructed all around it, increasing the total area to 285 square metres. What will be the width of the pathway?

What must be added to x² + 8x to make the expression a perfect square?

Find two consecutive odd numbers whose product is 195.

Without using a table of values, draw the graph of y = x² ? 4x + 2 and use it to solve the equation x² ? 4x = 5.

Solve for x ^if _x?⁶₄ = 1 + ⁴_x

If the sum of two numbers is 3 and the sum of their squares is 29, find the numbers.

Find the solution of the quadratic equation 8x² ? 34x + 21 = 0 by using the factorization method.

Solve for x if

Draw a graph of the function y = x² - 3x + 2 for the values of x from - 2 to 5.

From your graph, find:

(a) The range of the function?

(b) The minimum value of y and the value of x at which this minimum value occurs?

(c) The solution of the equation x² - 3x - 4 = 0

(d) The solution of the inequality x² - 3x + 2 > 0

(a) Factorize each of the following expressions:

1. 3a²c -5a ²d - 3b² c + 5b²d
2. 3(2 - y²)-17y

(b) Find the value of y which satisfies the equation 3(2 - y²) - 17y = 0 (6 marks)

Express the equation 2t^-10 - 3t^-5 + 1 = 0 in term of x where

(b)From the equation you obtained in part (a), find the value(s) of x that satisfy it by using the quadratic formula.

The length of a book exceeds its width by 5 cm. Calculate the dimensions of the hook given that its area is 50 cm²

Factorize the expression 6x² –11x +4 by splitting the middle term.

Solve the following Eqn. 4(p + 1)(1 - p)=3