Let's denote the roots of the equation as a and 4a (since one root is 4 times the other).

According to Vieta's formulas, the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a and the product of the roots is c/a.

In this case, the sum of the roots is a + 4a = 5a = -(-30)/2 = 15, so a = 15/5 = 3.

The product of the roots is a * 4a = 12a^2 = p/2. Substituting a = 3, we get p/2 = 12*3^2 = 108, so p = 2*108 = 216.

So, the value of p is 216.

Question

Let's denote the roots of the equation as a and 4a (since one root is 4 times the other).

According to Vieta's formulas, the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a and the product of the roots is c/a.

In this case, the sum of the roots is a + 4a = 5a = -(-30)/2 = 15, so a = 15/5 = 3.

The product of the roots is a * 4a = 12a^2 = p/2. Substituting a = 3, we get p/2 = 12*3^2 = 108, so p = 2*108 = 216.

So, the value of p is 216.

Knowee AI · Accepted Answer

Let's denote the roots of the equation as a and 4a (since one root is 4 times the other).

According to Vieta's formulas, the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a and the product of the roots is c/a.

In this case, the sum of the roots is a + 4a = 5a = -(-30)/2 = 15, so a = 15/5 = 3.

The product of the roots is a * 4a = 12a^2 = p/2. Substituting a = 3, we get p/2 = 12*3^2 = 108, so p = 2*108 = 216.

So, the value of p is 216.

If one root of the equation 2x2 – 30x + p = 0 is 4 times the other, then find the value of p.