Question

. If a & b are the zeros of a polynomial px2

– 5x + q, then the value of p & q, if a + b = ab = 10,

are a) 5 & ½ c) 5 & 2 c) ½ & 5 d) 10 & 1​

Answer 1

Answer:

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Step-by-step explanation:

the bus fare for the world in the house of

Answer 2

The values of p and q are (c) $\frac{1}{2}$  and  $5$ respectively.

Step-by-step explanation:

We are given a quadratic equation,

$px^{2} -5x+q=0$

a and b are the zeroes of equation, $a+b=10$ and $ab=10$.

we have to find the value of p and q.

• Formula used

General form of quadratic equation,

$ax^{2} +bx+c=0$

1. sum of zeroes $= \frac{-b}{a}$
2. product of zeroes $=\frac{c}{a}$

a is for coefficient of $x^{2}$  , b for coefficient of $x$  and c for constant.

• Calculation for p and q.

we have,

$px^{2} -5x+q=0$

by comparing this equation with general equation we get the values of a, b and c;

$a=p$  ,  $b=-5$  and $c=q$.

so the sum and product of zeroes by coefficient formula,

sum of zeroes $= \frac{-b}{a}$                             product of zeroes $=\frac{c}{a}$

                         $=\frac{-(-5)}{p}$                                                      $=\frac{q}{p}$

                         $=\frac{5}{p}$

we have the sum and product of zeroes,

$a+b=10$ and $ab=10$.

comparing the given sum and product of zeroes with calculated sum and product of zeroes by formula,

Sum of zeroes $=10$                           Product of zeroes $=10$

          $\frac{5}{p} =10$                                                           $\frac{q}{p}=10$

         $p=\frac{5}{10}$                                                              $q=10*p$

         $p=\frac{1}{2}$                                                               $q=10*\frac{1}{2}$

                                                                                 $q=5$

In this way we get the values of p and q $\frac{1}{2}$  and  $5$ respectively.