Problem 1 :

Solve the quadratic equation using quadratic formula :

x2 – 5x – 24 = 0

Problem 2 :

Solve the quadratic equation using quadratic formula :

x2 – 7x + 12 = 0

Problem 3 :

Solve the quadratic equation using quadratic formula :

15×2 – 11x + 2 = 0

Problem 4 :

Solve the quadratic equation using quadratic formula :

x + 1/x = 2½

Problem 5 :

Solve the quadratic equation using quadratic formula :

(x + 3)2 – 81 = 0

Problem 1 :

Solve the quadratic equation using quadratic formula :

x2 – 5x – 24 = 0

Solution :

The given quadratic equation is in the form of

ax2 + bx + c = 0

Comparing

x2 – 5x – 24 = 0

and

ax2 + bx + c = 0

we get

a = 1, b = -5 and c = -24

Substitute the above values of a, b and c into the quadratic formula.

Therefore, the solution is

{-3, 8}

Problem 2 :

Solve the quadratic equation using quadratic formula :

x2 – 7x + 12 = 0

Solution :

The given quadratic equation is in the form of

ax2 + bx + c = 0

Comparing

x2 – 7x + 12 = 0

and

ax2 + bx + c = 0

we get

a = 1, b = -7 and c = 12

Substitute the above values of a, b and c into the quadratic formula.

Therefore, the solution is

{3, 4}

Problem 3 :

Solve the quadratic equation using quadratic formula :

15×2 – 11x + 2 = 0

Solution :

The given quadratic equation is in the form of

ax2 + bx + c = 0

Comparing

15×2 – 11x + 2 = 0

and

ax2 + bx + c = 0

we get

a = 15, b = -11 and c = 2

Substitute the above values of a, b and c into the quadratic formula.

Therefore, the solution is

{2/5, 1/3}

Problem 4 :

Solve the quadratic equation using quadratic formula :

x + 1/x = 2½

Solution :

Write the given quadratic equation in the form :

ax2 + bx + c = 0

Then,

x + 1/x = 2½

x2/x + 1/x = 5/2

(x2 + 1)/x = 5/2

2(x2 + 1) = 5x

2×2 + 2 = 5x

2×2 – 5x + 2 = 0

Comparing

2×2 – 5x + 2 = 0

and

ax2 + bx + c = 0

we get

a = 2, b = -5 and c = 2

Substitute the above values of a, b and c into the quadratic formula.

Therefore, the solution is

{1/2, 2}

Problem 5 :

Solve the quadratic equation using quadratic formula :

(x + 3)2 – 81 = 0

Solution :

Write the given quadratic equation in the form :

ax2 + bx + c = 0

Then,

(x + 3)2 – 81 = 0

(x + 3)(x + 3) – 81 = 0

x2 + 3x + 3x + 9 – 81 = 0

x2 + 6x – 72 = 0

Comparing

x2 + 6x – 72 = 0

and

ax2 + bx + c = 0

we get

a = 1, b = 6 and c = -72

Substitute the above values of a, b and c into the quadratic formula.

Therefore, the solution is

{-12, 6}

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