Question

The roots of the equation x2 – 14x + 48 = 0 are

Answer 1

The quadratic equation x2 – 14x + 48 = 0 has two roots calculated using the quadratic formula. The roots are found to be x = 6 and x = 8 after following the formula and solving for x.

Step-by-step explanation:

The roots of the quadratic equation x2 – 14x + 48 = 0 can be found using the quadratic formula, which is x = –b ± √(b2 – 4ac) / (2a), where a, b, and c are coefficients from the equation ax2 + bx + c = 0.

In our case,

• a = 1
• b = -14
• c = 48

Plugging these values into the quadratic formula, we calculate the discriminant

b

2

– 4ac

, which is

196 – 4(1)(48) = 196 – 192 = 4

.

Next, we find the square root of the discriminant, √4, which is 2. Now, applying the quadratic formula, the roots are:

• x = (14 + 2) / 2 = 8
• x = (14 - 2) / 2 = 6

Therefore, the roots of the equation are

x = 6

and

x = 8

Answer 2

The roots of this equation will be x = 6 or x = 8.

You can solve this equation by factorising:

x² - 14x + 48 = 0

Factors of 48:

1 and 48

2 and 24

3 and 16

4 and 12

6 and 8

Because the x-coefficient is negative but the value at the end is positive, we know that both numbers in the brackets must be negative (i.e. (x - a)(x - b) ), so we need to find 2 numbers from the list of factors that when negative and added together give -14. In this case it is -6 and -8.

Therefore your final factorisation is (x - 6)(x - 8) = 0, which gives the solutions x = 6 or x = 8.

I hope this helps! Let me know if you have any questions :)