Class 10 Standard Form and Roots — practice questions with answers
Quadratic Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Which of the following is the standard form of a quadratic equation?
Aax + b = 0
Bax² + bx + c = 0, a not equal to 0
Cax³ + bx + c = 0
Dax² + bx + c = 0, a = 0
Show answer
Answer: B) ax² + bx + c = 0, a not equal to 0
A quadratic equation in standard form is ax² + bx + c = 0 where a, b, c are real and a is not 0.
2. The sum of the roots of x² - 7x + 10 = 0 is given by a−b. What is the sum of its roots?
A6
B8
C7
D14
Show answer
Answer: C) 7
Sum of roots = a−b=1−(−7)=7.
3. What is the sum of the coefficients a + b + c for the equation x² - 6x + 9 = 0?
A5
B8
C4
D3
Show answer
Answer: C) 4
a = 1, b = -6, c = 9, so a + b + c = 1 - 6 + 9 = 4.
4. A rectangular cricket practice net in Delhi has its length 5 m more than twice its breadth x. The area is 75 sq m. Which quadratic equation in standard form gives the breadth?
A2x² + 5x - 75 = 0
B2x² - 5x - 75 = 0
C2x² + 5x + 75 = 0
Dx² + 5x - 75 = 0
Show answer
Answer: A) 2x² + 5x - 75 = 0
Length = 2x + 5, area = x(2x + 5) = 75, so 2x² + 5x = 75, i.e. 2x² + 5x - 75 = 0.
5. In a class trip the number of girls is 1 more than the number of boys. If there are x boys, the product of the number of boys and the number of girls is 90. Write this as a quadratic equation in standard form and find the number of boys x.
A8
B18
C10
D9
Show answer
Answer: D) 9
Girls = x + 1, so x(x + 1) = 90 gives x² + x - 90 = 0 = (x - 9)(x + 10). Positive root x = 9 boys.