Question

Show your work to calculate the discriminant of the quadratic equation, and then state the number and type of solutions you expect the equation to have, based on the value of your discriminant.

Answer 1

0 = x^2 + 6x - 16

Answer 2

for a quadratic in the form
\[ax^2 + bx + c = 0\]

the discriminant is

\[\Delta = b^2 - 4ac\]

in your question a = 1, b = 6 and c = -16

so substitute them and get a value.

Answer 3

Thank you so much!

Answer 4

there are 3 different outcomes for the discriminant

\[\Delta > 0\]
the quadratic has 2 unequal real roots. If its a perfect square the roots are rational, otherwise there are irrational.

\[\Delta = 0\]

the quadratic has 2 equal or repeated roots, this is a perfect square.

\[\Delta < 0 \]

the quadratic has no real roots, meaning it is positive definite or negative definite

hope it helps

Answer 5

Wait, so all I have to do is substitute in the equation?

Answer 6

I will try it on my own and send you the answer to see if its right?

Answer 7

like this?

Answer 8

yes, subsitute into the formula and you get a number...

then match it to the conditions to determine the type of zeros..

well it didn't appear but its

\[\Delta = 6^3 - 4 \times 1 \times(-16) = 36 + 64\]

so what is the final number answer?

Answer 9

oops should be

\[\Delta = 6^2 - 4 \times 1 \times (-16) = 36 + 64\]

Answer 10

100?

Answer 11

great, so it meets the 1st condition, that there are 2 unequal roots.

100 is a perfect square 10^2 = 100 so the roots are rational

Answer 12

Okay, so what do I do for the other part of the question?

Answer 13

well you have done it.

(a) calculate you got 100

(b) the number and type, 100 > 0 so they are 2 unequal real roots. 100 is also a perfect square so they are rational roots

Answer 14

Thank you so so soooo much!!

Answer 15

I understand it now :)