find the values of 'P','Q', and 'R'.
(PX+Q)(2X+5)=6Xsquared+11X+R
the answer is p=3,q=-2,r=-10. how do I get these answers?
multiply the left side.
(Px+q)(2x+5)=6x^2 + 11x + R
2Px^2+2qx+6px+5q
2Px^2 + x(2q+6p)+5q=6x^2+11x + R
so 2P=6
and 5q=R
and (2q+6p)=11
you can solve those.
To find the values of 'P', 'Q', and 'R', you need to expand the given expression on the left side of the equation and then compare it with the right side of the equation.
Given equation: (PX + Q)(2X + 5) = 6X^2 + 11X + R
To expand the expression (PX + Q)(2X + 5), you need to use the distributive property. Multiply each term in the first parentheses by each term in the second parentheses.
Step 1: Multiply the first terms of each parentheses.
PX * 2X = 2PX^2
Step 2: Multiply the first term of the first parentheses by the second term of the second parentheses.
PX * 5 = 5PX
Step 3: Multiply the second term of the first parentheses by the first term of the second parentheses.
Q * 2X = 2QX
Step 4: Multiply the second terms of each parentheses.
Q * 5 = 5Q
Now, combine all of these terms to simplify the left side of the equation:
2PX^2 + 5PX + 2QX + 5Q = 6X^2 + 11X + R
By comparing the coefficients of 'X' on both sides of the equation, we get:
2P = 6 (coefficient of X^2)
5P + 2Q = 11 (coefficient of X)
5Q = R (constant term)
Now we have a system of three equations:
2P = 6
5P + 2Q = 11
5Q = R
To solve this system, we can start by solving the first equation for 'P':
2P = 6
Divide both sides by 2
P = 3
Substituting this value of 'P' in the second equation, we can solve for 'Q':
5P + 2Q = 11
5(3) + 2Q = 11
15 + 2Q = 11
2Q = 11 - 15
2Q = -4
Divide both sides by 2
Q = -2
Finally, substituting values of 'P' and 'Q' in the third equation, we can solve for 'R':
5Q = R
5(-2) = R
-10 = R
Therefore, the values of 'P', 'Q', and 'R' are P = 3, Q = -2, and R = -10.