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find the value of the discriminant. then describe the number and type of roots for the equation.
x^2 + x + 7 = 0

a. the discriminant is –29.
because the discriminant is less than 0, the two roots are complex.

b. the discriminant is 1.
because the discriminant is greater than 0 and is a perfect square, the two roots are real and rational.

c. the discriminant is –27.
because the discriminant is less than 0, the two roots are complex.

d. the discriminant is 27.
because the discriminant is greater than 0 and is a perfect square, the two roots are real and rational.

Use the discriminant to describe the roots of each equation. then select the best description. 2m2 + 3 = m double root real and rational roots real and irrational roots non-real roots

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Two rectangular prisms have the same volume. the area of the base of the blue prism is 418 4 1 8 square units. the area of the base of the red prism is one-half that of the blue prism. which statement is true?