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A) find the value of the discriminant

B) describe the number and type of roots

-3x^2-7x+2=6

Since a = -3, b = -7, and c = 2-6 = -4, they are all negative.

This gives a = -3, b = -7, and c = -4.

That is from the equation -3x² -7x - 4 = 0.

The discriminant is b² - 4ac. These values make it 49 - 48 = 1.

This makes the two factors be (7±1)/-6.

That gives 8/-6 and 6/-6, and these reduce to -4/3 and -1.

Looking at (x + 4/3)(x + 1) gives x² + 7x/3 + 4/3.

Multiplying by -3 gives -3x² - 7x - 4, which is what we started with.

Thus, it can be said there are two distinct real roots.

Algebra

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