# SOLUTION: How do I find the discriminant? The question ask to find {{{b^2-4ac}}} and the number of real solutions to each equation. 35. {{{4m^2+25 = 20m}}} 45. {{{x^2=x}}}

Algebra ->  Algebra  -> Radicals -> SOLUTION: How do I find the discriminant? The question ask to find {{{b^2-4ac}}} and the number of real solutions to each equation. 35. {{{4m^2+25 = 20m}}} 45. {{{x^2=x}}}      Log On

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 Question 157288This question is from textbook elementary and intermediate algebra : How do I find the discriminant? The question ask to find and the number of real solutions to each equation. 35. 45. This question is from textbook elementary and intermediate algebra Found 2 solutions by Edwin McCravy, SAT Math Tutor:Answer by Edwin McCravy(8880)   (Show Source): You can put this solution on YOUR website!How do I find the discriminant? The question ask to find and the number of real solutions to each equation. 35. 45. ``` You must first rearrange the equations so that 0 appears on the right and the three terms on the left are in descending order like this: , or whatever the letter of the unknown happens to be: That's the only way you can tell what to substitute for , , and in the formula: ------- For your problem 35: You must first get a 0 on the right side by adding to both sides: And you must write the left side in descending order, like this: Then when you compare that to , it is easy to see that ,, and . So then you can easily substitute those values in the expression for the discriminant: When the discriminant is 0, there is exactly 1 real solution. So this particular quadratic equation has 1 real solution. If it were negative there would be no real solutions, and if it were positive there would be exactly two real solutions. --------------------------------- For your problem 45: You must first get a 0 on the right side by adding to both sides: But the left side contains only two terms! So you must add on a to the left side: Also it may be helpful to write the understood 's before and , like this: The left side is already in descending order, so when you compare that to , it is easy to see that ,, and . So then you can easily substitute those values in the expression for the discriminant: Since the discriminant is a positive number, there are exactly two real solutions. Edwin``` Answer by SAT Math Tutor(36)   (Show Source): You can put this solution on YOUR website!Begin by setting up a quadratic equation equal to zero so: 35. 4m^2 - 20m + 25 = 0 45. x^2 - x = 0 Then, label a, b, and c which are the coefficients: 35. a = 4, b = -20, c = 25 45. a = 1, b = -1, c = 0 Then, use the discriminant formula b^2 - 4ac: 35. (-20)^2 - 4(4)(25) = 0 45. 1^2 - 4(1)(0) = 1