Answer:4x+32+5x-15
Step-by-step explanation: that’s the simplified equation, you would just have to distribute the 4 to its own equation and the 5 into its own equation.. but i think the second part of ur question is missing..
Answer:
8p +56 +16q
Step-by-step explanation:
8 (p+7+2q)
If we distribute the 8 into everything in the parenthesis, we get:
8p +56 +16q
Answer:
I cant see that, its upside down.
Step-by-step explanation:
Answer:
Roots are not real
Step-by-step explanation:
To prove : The roots of x^2 +(1-k)x+k-3=0x
2
+(1−k)x+k−3=0 are real for all real values of k ?
Solution :
The roots are real when discriminant is greater than equal to zero.
i.e. b^2-4ac\geq 0b
2
−4ac≥0
The quadratic equation x^2 +(1-k)x+k-3=0x
2
+(1−k)x+k−3=0
Here, a=1, b=1-k and c=k-3
Substitute the values,
We find the discriminant,
D=(1-k)^2-4(1)(k-3)D=(1−k)
2
−4(1)(k−3)
D=1+k^2-2k-4k+12D=1+k
2
−2k−4k+12
D=k^2-6k+13D=k
2
−6k+13
D=(k-(3+2i))(k+(3+2i))D=(k−(3+2i))(k+(3+2i))
For roots to be real, D ≥ 0
But the roots are imaginary therefore the roots of the given equation are not real for any value of k.
Take out the constants
(2 × 4)x^2xx^2y^3y^4z^2
Simplify 2 × 4 to 8
8x^2xx^2y^3y^4z^2
Use the Product Rule: x^ax^b = x^a + b
8x^2 + 1 + 2y^3 + 4z^2
Simplify 2 + 1 + 2 to 5
8x^5y^3 + 4z^2
Simplify 3 + 4 to 7
<u>8x^5y^7z^2</u>