Question

If y - 2 and y - 1/2 are the factors of py^2 + 5y + r then

Answer 1

Step-by-step explanation:

The equation have two zeore 2 and 1/2

By putting the value of y

Equation will be =4p+10+r

Answer 2

The correct answer is the value of p is -2 and r is -2.

Given: Factors of equation = y-2 and $y-\frac{1}{2}$.

Equation = $py^{2} +5y+r$.

To Find: The value of p and r.

Solution:

If y-2 and $y-\frac{1}{2}$ are the factors of $py^{2} +5y+r$. Then their multiplication should be equal to the equation.

= (y - 2)(y - $\frac{1}{2}$)

= $y^{2} -2y-\frac{y}{2}+1$

$y^{2} -\frac{5y}{2}+1$ = 0

Multiply the equation by -2. As the RHS is 0 it will not effect the equation.

$-2(y^{2} -\frac{5y}{2}+1)$ = 0

$-2y^{2} -(-2)\frac{5y}{2}-2$ = 0

$-2y^{2} +5y-2$ = 0

Now compare both the equations.

By comparing coefficient of $y^{2}$.

p = -2

By comparing constants.

r = -2

Hence, the value of p is -2 and r is -2.

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