Solve each quadratic equation using the quadratic formula. See...

Question

Solve each quadratic equation using the quadratic formula. See Example 7.

-3x² + 6x + 5 = 0

Accepted Answer

Welcome back everyone. In this problem, we want to find the roots of the quadratic equation negative four X squared plus eight X plus eight equals zero. By applying the quadratic formula. A says X equals one plus or minus two root three, B one plus R minus root three, C one plus R minus two root two and D one plus R minus three root two. Now what do we know that can help us to find the roots using the quadratic formula? We'll recall that the quadratic formula says that for a quadratic equation in the form AX squared plus BX plus C equals zero, the general form then AX its roots are going to be equal to negative B plus or minus the square root of B squared minus four AC all divided by two A. Now, from our equation here, from our own quadratic equation negative four X squared plus eight X plus eight, we can tell that A, the coefficient of X squared equals negative four B, the coefficient of X equals eight and C, the constant also equals it. So since we have our values A B and C, we should be able to plug them into the quadratic formula and thus solve for the roots. But before we solve, we first need to calculate the discriminant that is the expression under the square root in the quadratic equation. And this is important because the roots exist only if the discriminant exists. OK? No, are discriminant. OK. The discriminant which is gonna be equal to B squared minus four AC is going to be equal to eight squared minus four, multiplied by negative four, multiplied by eight, eight squared is 64 negative four, multiplied by negative four is 16 and 16, multiplied by eight is 128 and 6464 plus 128 equals 192. So this tells us that the discriminant exists. Thus, we can solve for the roots because now that means X is going to be equal to negative B so that negative eight plus or minus the square root of 192 divided by two multiplied by negative four. OK? And now when we go ahead and solve here, that's going to be negative eight plus R minus eight root three. That's the, that's what the square of 192 would work out to be. And that's all divided by negative eight. Now, if we divide both of our terms by negative eight here because they both have a factor of eight, negative eight divided by negative eight equals one. OK. And now we're going to have that plus or minus eight root three divided by negative eight which will leave us with root three. OK. Therefore, the correct answer is X equals one plus R minus root three. B is the correct choice. Thanks for watching everyone. I hope this video helped.

Solve each quadratic equation using the quadratic formula. See Example 7.

-3x² + 6x + 5 = 0

Key Concepts

Quadratic Equations

Quadratic Formula

Discriminant

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