The discriminant is 164 and there are two real solutions.
What is Quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax^2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
We can find the discriminant as shown below:
x^2+14x+8=0
a=1, b=14, c=8
Discriminant=b^2-4ac
=(14)^2-4*1*8
=196-32
=164>0
As the discriminant is positive and greater than zero. So, there are two real and distinct solution.
Hence, discriminant is 164 and two real solution.
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ANSWER
EXPLANATIONSolve for x, noting that scalar multiplication on matrices is distributive:
![\begin{aligned} 4X + 5A &= B \\ 4X &= B + (-5A) \\ X &= \tfrac{1}{4}( B + (-5A) ) \\ X &= \tfrac{1}{4} B + (-\tfrac{5}{4}A) \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%0A4X%20%2B%205A%20%26%3D%20B%20%5C%5C%20%0A4X%20%26%3D%20B%20%2B%20%28-5A%29%20%5C%5C%0AX%20%26%3D%20%5Ctfrac%7B1%7D%7B4%7D%28%20B%20%2B%20%28-5A%29%20%29%20%5C%5C%0AX%20%26%3D%20%5Ctfrac%7B1%7D%7B4%7D%20B%20%2B%20%28-%5Ctfrac%7B5%7D%7B4%7DA%29%0A%5Cend%7Baligned%7D)
Note that
![\begin{aligned} \tfrac{1}{4} B &= \frac{1}{4} \begin{bmatrix} 4 & -8 \\ 2 & -1 \\ 9 & 1 \end{bmatrix} \\ \\ &= \begin{bmatrix} (1/4) \cdot 4 & (1/4) \cdot-8 \\ (1/4) \cdot2 & (1/4)\cdot-1 \\ (1/4)\cdot9 & (1/4)\cdot1 \end{bmatrix} \\ \\ &= \begin{bmatrix} 1 & -2 \\ 1/2 & -1/4\\ 9/4 & 1/4\end{bmatrix} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Ctfrac%7B1%7D%7B4%7D%20B%20%26%3D%20%5Cfrac%7B1%7D%7B4%7D%20%5Cbegin%7Bbmatrix%7D%204%20%26%20-8%20%5C%5C%202%20%26%20-1%20%5C%5C%209%20%26%201%20%5Cend%7Bbmatrix%7D%20%5C%5C%20%5C%5C%20%26%3D%20%5Cbegin%7Bbmatrix%7D%20%281%2F4%29%20%5Ccdot%204%20%26%20%281%2F4%29%20%5Ccdot-8%20%5C%5C%20%281%2F4%29%20%5Ccdot2%20%26%20%281%2F4%29%5Ccdot-1%20%5C%5C%20%281%2F4%29%5Ccdot9%20%26%20%281%2F4%29%5Ccdot1%20%5Cend%7Bbmatrix%7D%20%5C%5C%20%5C%5C%20%26%3D%20%5Cbegin%7Bbmatrix%7D%201%20%26%20-2%20%5C%5C%201%2F2%20%20%26%20-1%2F4%5C%5C%209%2F4%20%26%201%2F4%5Cend%7Bbmatrix%7D%20%5Cend%7Baligned%7D)
and
![\begin{aligned} (-\tfrac{5}{4}A) &= -\frac{5}{4} \begin{bmatrix} 0 & -3 \\ -6 & -8 \\ 5 & -9 \end{bmatrix} \\ \\ &= \begin{bmatrix} (-5/4)\cdot 0 &(-5/4)\cdot -3 \\ (-5/4)\cdot-6 &(-5/4)\cdot -8 \\ (-5/4)\cdot5 &(-5/4)\cdot -9 \end{bmatrix} \\ \\ &= \begin{bmatrix} 0 & 15/4 \\ 15/2 & 10 \\ -25/4 & 45/4 \end{bmatrix} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%0A%28-%5Ctfrac%7B5%7D%7B4%7DA%29%20%26%3D%20%0A-%5Cfrac%7B5%7D%7B4%7D%0A%5Cbegin%7Bbmatrix%7D%0A0%20%26%20-3%20%5C%5C%0A-6%20%26%20-8%20%5C%5C%0A5%20%26%20-9%0A%5Cend%7Bbmatrix%7D%0A%5C%5C%20%5C%5C%0A%26%3D%20%5Cbegin%7Bbmatrix%7D%0A%28-5%2F4%29%5Ccdot%200%20%26%28-5%2F4%29%5Ccdot%20-3%20%5C%5C%0A%28-5%2F4%29%5Ccdot-6%20%26%28-5%2F4%29%5Ccdot%20-8%20%5C%5C%0A%28-5%2F4%29%5Ccdot5%20%26%28-5%2F4%29%5Ccdot%20-9%0A%5Cend%7Bbmatrix%7D%0A%5C%5C%20%5C%5C%0A%26%3D%20%5Cbegin%7Bbmatrix%7D%0A0%20%26%2015%2F4%20%5C%5C%0A15%2F2%20%26%2010%20%5C%5C%0A-25%2F4%20%26%2045%2F4%0A%5Cend%7Bbmatrix%7D%0A%5Cend%7Baligned%7D%20)
Therefore, since we add corresponding entries with matrix addition:
Answer:
Step-by-step explanation:
Brother, it's 253 there are trapezoid calculators.
Answer:
-3/35
Step-by-step explanation:
Make -3 1/2 into an improper fraction
3/10 divided by -7/2
Multiply
3/10 * -2/7
= -6/70
Simplify
-3/35
Hope this helps! :)
Answer: x=5
Step-by-step explanation:sorry I just solve it on the paper and I don't have time to write it the step by step