Quadratic Equations Test

Result

Quadratic Equations Test - 4

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Question 1
1 / -0

Each side of a square measures 4 cm more than each side of another square. If the sum of their areas is 400 sq. cm, then what is the area of the larger square?

A
144 cm²

B
169 cm²

C
196 cm²

D
256 cm²

Solution

Let each side of the smaller square measure x cm.
Then, length of each side of the larger square = (x + 4) cm

According to problem:
(x + 4)² + x² = 400 {Area of square = Side × Side}

x² + 8x + 16 + x² = 400
Or 2x² + 8x - 384 = 0
⇒ x² + 4x - 192 = 0

Or (x + 16)(x - 12) = 0
⇒ x = 12
So, length of each side of the larger square = (12 + 4) cm = 16 cm

Area = (16)² cm²= 256 cm²
Question 2
1 / -0

B's age is the square of the age of A. After 5 years, B will be 3 times as old as A. What is the difference between their ages?

A
5 years

B
10 years

C
15 years

D
20 years

Solution

Let the age of A be x.
So, B's age = x²

After 5 years, x² + 5 = 3(x + 5)
x² + 5 – 3x – 15 = 0

x² – 3x – 10 = 0 ⇒ x = -2, 5
x is +ve, so x = 5

So, A's age = 5 years
B's age = 25 years

Difference = (25 – 5) years = 20 years
Thus, answer option 4 is correct.
Question 3
1 / -0

Read the following statements carefully and choose the suitable.

Statement I: The quadratic equation ax² + bx + c = 0 has no real roots if b² - 4ac > 0.
Statement II: The number of possible values of m (m is a whole number) is 5 if the quadratic equation 4x² + 16x + 4m = 0 has real roots.

A
Both statements I and II are true.

B
Statement I is true, but statement II is false.

C
Statement I is false, but statement II is true.

D
Both statements I and II are false.

Solution

Statement I is false because if the quadratic equation ax² + bx + c = 0 has no real roots, then b² - 4ac < 0.

Statement II is true because for the equation 4x² + 16x + 4m = 0 to have real roots, b² – 4ac must be greater than or equal to 0, i.e. 256 - 64m ≥ 0 or 4 ≥ m, m being a whole number.

So, m can have 0, 1, 2, 3 and 4 as possible values. So, 5 values are possible for m.