If α and β are the roots of the expression 2x2 + 8x + 7 = 0, write down the value of pα2 + β2 + 1

To solve this problem, we first need to find the roots of the equation 2x^2 + 8x + 7 = 0.

Step 1: Find the roots of the equation The roots of a quadratic equation ax^2 + bx + c = 0 are given by the formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Here, a = 2, b = 8, and c = 7.

So, the roots are:

α, β = [-8 ± sqrt((8)^2 - 427)] / 2*2 = [-8 ± sqrt(64 - 56)] / 4 = [-8 ± sqrt(8)] / 4 = [-8 ± 2sqrt(2)] / 4 = -2 ± sqrt(2)

So, the roots are α = -2 + sqrt(2) and β = -2 - sqrt(2).

Step 2: Find the value of pα^2 + β^2 + 1 We need to find the value of pα^2 + β^2 + 1. But we don't have the value of p. Without the value of p, we can't find the exact value of this expression.

If p is given, we can substitute the values of α and β into the expression to find the value.