Question

If 2 and ½ are the zeros of px2 + 5x + r, then
(a) p = r = 2
(b) p = r = - 2
(c) p = 2, r= -2
(d) p = -2, r=2​

Answer 1

Answer:

p = r = 2

Step-by-step explanation:

sum of zeroes

2 +1/2 = 5/p

5/2 = 5/p

p = 2

product of zeroes

2*1/2 = r/p

1 = r/ 2

r = 2

therefore, p = r = 2

PLEASE MARK AS BRAINLEIST

Answer 2

Given: 2 and 1/2 are the zeroes of $px^{2} +5x+r$.

To Find: The required solution of p and r of the quadratic polynomial.

Solution:

• The general form of the quadratic polynomial is, $ax^{2} +bx+c,a\neq 0$.
• The sum of the roots of quadratic polynomial is $\alpha +\beta =\frac{-b}{a}$ $=\frac{-5}{p}$
• Since, 2 and 1/2 are the zeroes of polynomial,
• $2+\frac{1}{2}$$=\frac{-5}{p}$
• $\frac{4+1}{2}=\frac{-5}{p}$
• $\frac{5}{2}=\frac{-5}{p}$
• Transpose $p$ to left and $\frac{5}{2}$ to right.
• $p=-5$×$\frac{2}{5}$
• $p=-2$
• The product of the roots of quadratic polynomial is $\alpha .\beta =\frac{c}{a}$
• $2$×$\frac{1}{2}$$=\frac{r}{p}$
• Substitute $p=-2$
• $\frac{2}{2}=\frac{r}{-2}$
• $1=\frac{r}{-2}$
• $r=-2$
• Therefore, if $2$ and $\frac{1}{2}$ are the zeroes of $px^{2} +5x+r$, then (b) $p=r=-2$