discriminants of quadratic equation??? explain?

Question

which # is the discriminant of a quadratic equation whose roots are real, unequal, and irrational?
a. 0
b.7
c.-5
d.4

plzzzz explain thanks

Answer 1

it's (b) 7.

the discriminant is the b^2 - 4ac that appears in the quadratic formula. if the discriminant is negative, then there are no real roots, and if it's zero, then there is only one distinct root. if it's positive, then there are two distinct roots.

since the quadratic formula requires you to take the square root of the discriminant, you'll get irrational roots if the square root of the discriminant is irrational.

so out of the four answers, the only one that's positive and has an irrational square root is 7.

Answer 2

b. 7

The discriminant of a quadratic equation is the portion of the quadratic formula found inside the square root sign. It is:
b^2 - 4*a*c

If this number is 0, then there will be no second term of the formula, and therefore no (+/-). The two roots will be the same. This eliminates a.

If the number is negative, then the roots are imaginary, because the square root of a negative number is not real. This eliminates c.

In order for the roots to be irrational, the square root must be irrational, and the discriminant must not be a perfect square. This eliminates d, because 4 is a perfect square.

That leaves us with (b).

Answer 3

If the discriminant is 0, the roots are real and equal.
If the discriminant is -5 the roots are complex.
If the discriminant is 4, the roots are rational,
since 4 is a square.
That leaves b. 7 as the answer.

Answer 4

The discrimiant of a quadratic equation is the expression b^2 - 4ac, where a,b and c are the coefficients of ax^2 + bx + c If b^2 - 4ac > 0, then the equation has two real roots If b^2 - 4ac = 0, then the equation has one real root If b^2 - 4ac < 0, then the equation has no real roots The x-intercepts of every graph occurs at y=0, so to obtain the x-intercepts of a quadratic equation you need to solve ax^2 + bx + c = 0, where the solution is generally given by the formula x = [-b +/- sqrt(b^2 - 4ac)] / 2a

Answer 5

b. 7. <-- answer
0 produces a double root (each root has same value).
- 5 will produce non-real solution (invlves sqrt(-1)
4 is a perfect square so roots will be rational
7 involves the sqrt(7) which is irrationalso roots will be irrational, unequal and real. It's the answer.