Step-by-step explanation:
The quadratic equation is x² + (p - 5)x + 2q = 0.
By Vieta's Formula,
we have SOR = -b/a and POR = c/a.
=> (-3) + (6) = -(p - 5) and (-3)(6) = 2q.
=> 3 = 5 - p and -18 = 2q
Hence, p = 2 and q = -9.
Alternate Method:
We have (x + 3) and (x - 6) as factors of the quadratic equation x² + (p - 5)x + 2q = 0.
=> (x + 3)(x - 6) = x² - 3x - 18.
By Comparing Coefficients,
(p - 5) = -3 and 2q = 18.
Hence p = 2 and q = -9.
Using y=Mx+b, the answer is y=10x-4.
Answer:
x²-5x+6
Step-by-step explanation:
The question is to find product in : x(x-2)+3(2-x)-----------(a)
Make terms in brackets same by introducing a negative sign as;
Collect like terms as : x(x-2) - 3 (x-2)------------ (b)
Note that expression (a) is similar to (b)
Factorize equation (b) as : (x-3)(x-2)
Distribute as : x(x-2) -3 (x-2 ) ------ x²-2x-3x+6
Collect like terms as: x²-5x+6
Final expression : x²-5x+6
Testing with x=5 in original expression
x(x-2)+3(2-x)
5(5-2)+3(2-5)
25-10+6-15
25+6-10-15
31-10-15=6
Using the final expression;
x²-5x+6
5²-5(5)+6
25-25+6
=6
25 because 4 - 3 is one, or one 25.... the answer is 25
