Solving this equation

Qwertyuiop[]

Qwertyuiop[]

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Jun 1, 2022
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Hi, I have this equation which is a product of one quadratic and a quartic equation. I set them equal to 0 and solved the quadratic easily. For the quartic i used substitution and then obtained a quadratic. Using the discriminant for the quadratic i found a negative answer so it has no real solutions. Now the quadratic has solutions but the quartic has no solutions, what is going to happen to the composite equation ? It will only have the quadratic solution right ? So the answer must be 2 and only 2 real solutions, option (b). I just need to confirm if i am right . Is there another way to find the correct answer?
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Let's replace the quartic equation by a constant. E.g. 5. 5=0 has no solutions. What will be the solutions of the composite equation?
 
A product of two factors is 0 if and only if one (or both) of the factors equal 0. Since the 2nd can't be zero, then a solution can only come from the 1st factor.

I think that things might become clearer if you can please tell me what (x+2)(x+7) equals if x=3.
 
Qwertyuiop[] said:
Hi, I have this equation which is a product of one quadratic and a quartic equation. I set them equal to 0 and solved the quadratic easily. For the quartic i used substitution and then obtained a quadratic. Using the discriminant for the quadratic i found a negative answer so it has no real solutions. Now the quadratic has solutions but the quartic has no solutions, what is going to happen to the composite equation ? It will only have the quadratic solution right ? So the answer must be 2 and only 2 real solutions, option (b). I just need to confirm if i am right . Is there another way to find the correct answer?
Click to expand...
Nice reasoning.
 
Steven G said:
A product of two factors is 0 if and only if one (or both) of the factors equal 0. Since the 2nd can't be zero, then a solution can only come from the 1st factor.

I think that things might become clearer if you can please tell me what (x+2)(x+7) equals if x=3.
Click to expand...
I will answer my question as I think it is important to see what is going on.
If x=3, then (x+2)(x+7) becomes (3+2)(3+7)=(5)(10). Many times the response I get to such a question is the answer is 5 and 10. NO. The answer is 5 times 10 or 50. You are to multiply these factors together. If the product happened to be 0, then at least one of the factors is 0! Even if the factors are more complicated than real numbers if the product is 0, then one or both factors must be 0.
 
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