Mathematics, 31.08.2019 13:30 01030901

What two numbers add to 18 and multiply to 82

Answers: 2

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Answer from: bray40

The answers are complex numbers...

Here's why...

p+q=18

pq=82

Therefore:

p=18-q

p=82/q

Therefore:

18-q=82/q

q(18-q)=q(82/q)

18q-q²=82

(-1)(18q-q²)=82(-1)

q²-18q=-82

(q-9)²-9²=-82

(q-9)²-81=-82

(q-9)²=-82+81

(q-9)²=-1

q-9=-√(-1)=-i

q-9=√(-1)=i

Therefore:

q=9-i

q=9+i

ANSWERS:

When q=9-i, p=9+i

When q=9+i, p=9-i

Proof:

p+(9-i)=18

p+9-i=18

p=18-9+i

p=9+i

p+(9+i)=18

p+9+i=18

p=18-9-i

p=9-i

More proofs:

p=82/(9+i)

p=(82/(9+i))*((9-i)/(9-i))

p=(82(9-i))/(81-9i+9i-i²)

p=(82(9-i))/(81-(-1))

p=(82(9-i))/82

p=9-i

p=82/(9-i)

p=(82/(9-i))*((9+i)/(9+i))

p=(82(9+i))/(81+9i-9i-i²)

p=(82(9+i))/(81-(-1))

p=(82(9+i))/82

p=9+i

Answer from: johnsonwhitney2

$x^2 +18x + 82\\\\ \frac{-b \pm \sqrt{ b^2 -4( a)(c)} }{2(a)}\\\\ \frac{-18\pm \sqrt{18^2 -4(1)(82)} }{2(1)}\\\\ \frac{-18\pm \sqrt{-4 } }{2} = \frac{-18\pm \sqrt{-4\times1 } }{2} \\\\ = \frac{-18\pm 2i\sqrt{1 } }{2} \\\\ = \frac{-9\pm 1i\sqrt{1 } }{1} \\\\ = -9\pm 1i\sqrt{1 }\\\\\boxed{\bf{=-9 \pm i}}$

The two numbers that add to 18 and multiply to 82 are 9 + i and 9 - i.

(9 + i)(9 - i) = 9^2 - i^2 = 81 - (-1) = 81 + 1 = 82
(9 + i) + (9 - i) = 9 + i + 9 - i = 9 + 9 + i - i = 18

Answer from: Quest

Hello!

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

why?

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

$3x-6$

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

$3x-6=0$

$3x=6$

$x=\frac{6}{3}=2$

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

Answer from: Quest

step-by-step explanation:

(3rd option) - c

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What two numbers add to 18 and multiply to 82...

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