<h3><u>Correct Questions :- </u></h3>
Find the values of P for which the quadratic equation 4x²+px+3=0 , provided that roots are equal or discriminant is zero .
<h3><u>Solution</u>:- </h3>
Let us Consider a quadratic equation αx² + βx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.
For equal roots
![\quad\green{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}}](https://tex.z-dn.net/?f=%5Cquad%5Cgreen%7B%20%5Cunderline%20%7B%20%5Cboxed%7B%20%5Csf%7BDiscriminant%2C%20D%20%3D%20%CE%B2%C2%B2%20-%204%CE%B1c%7D%7D%7D%7D%20)
So,
![\sf{ β² - 4αc = 0}](https://tex.z-dn.net/?f=%5Csf%7B%20%20%CE%B2%C2%B2%20-%204%CE%B1c%20%3D%200%7D)
Here,
Now,
![\begin{gathered}\implies\quad \sf p²- 4 \times 4 \times 3 =0 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cimplies%5Cquad%20%5Csf%20%20p%C2%B2-%204%20%5Ctimes%204%20%5Ctimes%203%20%3D0%20%5Cend%7Bgathered%7D%20)
![\begin{gathered}\implies\quad \sf p²- 48 =0 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cimplies%5Cquad%20%5Csf%20%20p%C2%B2-%2048%20%3D0%20%5Cend%7Bgathered%7D%20)
![\begin{gathered}\implies\quad \sf p²=48\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cimplies%5Cquad%20%5Csf%20%20p%C2%B2%3D48%5Cend%7Bgathered%7D%20)
![\begin{gathered}\implies\quad \sf p=±\sqrt{48}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cimplies%5Cquad%20%5Csf%20%20p%3D%C2%B1%5Csqrt%7B48%7D%5Cend%7Bgathered%7D%20%20)
![\begin{gathered}\implies\quad \sf p=±\sqrt{2 \times 2 \times 2 \times 2 \times 3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cimplies%5Cquad%20%5Csf%20%20p%3D%C2%B1%5Csqrt%7B2%20%5Ctimes%202%20%5Ctimes%202%20%5Ctimes%202%20%5Ctimes%203%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered}\implies\quad \sf p=± 2\times 2\sqrt{ 3 }\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cimplies%5Cquad%20%5Csf%20%20p%3D%C2%B1%202%5Ctimes%202%5Csqrt%7B%203%20%7D%5Cend%7Bgathered%7D%20)
![\begin{gathered}\implies\quad \boxed{\sf{p=±4\sqrt{ 3 }}}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cimplies%5Cquad%20%5Cboxed%7B%5Csf%7Bp%3D%C2%B14%5Csqrt%7B%203%20%7D%7D%7D%5Cend%7Bgathered%7D%20)
Thus, the values of P for which the quadratic equation 4x²+px+3=0 are-
4√3 and -4√3.
C 28 square meters smokejumper
Answer:
C
Step-by-step explanation:
15 times 2 is 30
1 times 2 is 2
Proportinal
Hope this helps
Answer: ![p=7, q=3](https://tex.z-dn.net/?f=p%3D7%2C%20q%3D3)
Step-by-step explanation:
The midline of the function is
![\frac{10-4}{2}=3 \implies q=3](https://tex.z-dn.net/?f=%5Cfrac%7B10-4%7D%7B2%7D%3D3%20%5Cimplies%20q%3D3)
This means that to obtain a maximum of 10, when
reaches it's maximum, 1, ![g(x)=p+q=10 \implies p=7](https://tex.z-dn.net/?f=g%28x%29%3Dp%2Bq%3D10%20%5Cimplies%20p%3D7)