Question

Use the discriminant to determine the number of real solutions of the equation. Do not solve the equation.
x 2 - 4.91x + 3.86 = 0

Answer 1

Do you know the formula of the discriminant and the output value in comparison to real numbers and imaginary numbers?

Answer 2

no

Answer 3

Google is your best friend.

but in this case, The discriminant is the formula that is written under the square root of the quadratic formula:
\[b ^{2} - 4(a)(c)\]

this is your original equation: \[x ^{2} -4.91x + 3.86 = 0\] the regular form of a quadratic equation\[a x^{2} + bx + c = 0\]
do you see a resemblance? take the value in the spot of "a" and the value in spot of "b" and "c" (don't forget the negatives) and plug them into the discriminant. Then use the output value. If it's above "0" then you have two real roots, if it's below "0" then you have two imaginary numbers.

Answer 4

that just confused me more. when I did the quadratic formula I got x=3.93 ,0.98

Answer 5

Don't use the quadratic formula. Use only the "discriminant" which equals the above formula I posted. And then ask yourself if the final answer from your "discriminant", negative or positive.

Answer 6

the discriminant I got Is 8.67

Answer 7

Excellent. Now compare that to the first reply I gave you at the very bottom of the paragraph. That will answer your question in your opening question.

Cheers.

Answer 8

so its just two real roots

Answer 9

Basically yes. You just solve them earlier in this thread. ;)
Look up discriminants and real values and imaginary numbers online. It will give you pictures and definitions that will expand your knowledge.

Cheers.