SOLUTION: Hi! Please anybody just help me with my works. Thank you very much in advance for any of your help. (a) Use the quadratic formula to solve the equation 3p2 + 5p — 11 = 0. Giv

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi! Please anybody just help me with my works. Thank you very much in advance for any of your help. (a) Use the quadratic formula to solve the equation 3p2 + 5p — 11 = 0. Giv      Log On


   

Question 770382: Hi! Please anybody just help me with my works. Thank you very much in advance for any of your help.
(a) Use the quadratic formula to solve the equation
3p2 + 5p — 11 = 0.
Give your answers correct to two decimal places.
MY ANSWER: 1.25 and -2.92 are these correct?
(b) Find the discriminant of the quadratic expression 7x2 — 3x — 11.
MY ANSWER: d=317 is it correct?
(c) Write the quadratic expression x2 — 34x + 9 in completed-square
form.
MY ANSWER: (x-7)^2=280 is it correct?
(d) Use the completed-square form from part (c) to solve the equation x2 — 34x + 9 = 0, leaving your answer in exact (surd)form.
MY ANSWER: x1=7+2surd70 and x2=7-2surd70 are these correct?
(e) Use the completed-square form from part (d) to write down the
vertex of the parabola y = x2 — 34x + 9
MY ANSWER: y=-280 x=7 are these correct?


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(a) Use the quadratic formula to solve the equation
3p2 + 5p — 11 = 0.
Give your answers correct to two decimal places.
MY ANSWER: 1.25 and -2.92 are these correct?
============================
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B5x%2B-11+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A3%2A-11=157.

Discriminant d=157 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+157+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+157+%29%29%2F2%5C3+=+1.25499401435694
x%5B2%5D+=+%28-%285%29-sqrt%28+157+%29%29%2F2%5C3+=+-2.92166068102361

Quadratic expression 3x%5E2%2B5x%2B-11 can be factored:
3x%5E2%2B5x%2B-11+=+%28x-1.25499401435694%29%2A%28x--2.92166068102361%29
Again, the answer is: 1.25499401435694, -2.92166068102361. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B5%2Ax%2B-11+%29


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It's correct to 2 places.
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(b) Find the discriminant of the quadratic expression 7x2 — 3x — 11.
MY ANSWER: d=317 is it correct?
Disc = b^2 - 4ac = 9 + 4*(7*11) = 317
===============================================
(c) Write the quadratic expression x2 — 34x + 9 in completed-square
form.
MY ANSWER: (x-7)^2=280 is it correct?
-----
x%5E2+-+34x+%2B+9+=+%28x+-+17%29%5E2+%2B+280
Not (x-7)^2
-------------------
(d) Use the completed-square form from part (c) to solve the equation x2 — 34x + 9 = 0, leaving your answer in exact (surd)form.
MY ANSWER: x1=7+2surd70 and x2=7-2surd70 are these correct?
Use sqrt, not surd
Use ^ for exponents, Shift 6
--------------
x^2 - 34x + 9 = 0
+x%5E2+-+34x+=+-9
x%5E2+-+34x+%2B+289+=+-9+%2B+289+=+280
%28x+-+17%29%5E2+=+280
x-17+=+sqrt%28280%29
x+-17+=+-sqrt%28280%29
=====================================
(e) Use the completed-square form from part (d) to write down the
vertex of the parabola y = x2 — 34x + 9
MY ANSWER: y=-280 x=7 are these correct?