Question

The equation px2 - 50x + 75 = 0 has
two distinct roots.
Also, one of the roots is 9 times the
other.
Find the value of p.
p=​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{The equation}\;\mathsf{px^2-50x+75=0}$

$\textsf{has two distinct roots}$

$\underline{\textsf{To find:}}$

$\textsf{The value of p}$

$\underline{\textsf{Solution:}}$

$\textsf{Let the roots be a and 9a}$

$\textsf{Then,}$

$\textsf{Sum of the roots:}$

$\mathsf{a+9a=\dfrac{50}{p}}$

$\mathsf{10\,a=\dfrac{50}{p}}$

$\mathsf{a=\dfrac{5}{p}}$......(1)

$\textsf{Product of the roots:}$

$\mathsf{a(9a)=\dfrac{75}{p}}$

$\mathsf{9a^2=\dfrac{75}{p}}$

$\mathsf{3a^2=\dfrac{25}{p}}$.....(2)

$\textsf{Using (1) in (2), we get}$

$\mathsf{3(\dfrac{5}{p})^2=\dfrac{25}{p}}$

$\mathsf{3(\dfrac{25}{p^2})=\dfrac{25}{p}}$

$\mathsf{\dfrac{3}{p^2}=\dfrac{1}{p}}$

$\mathsf{\dfrac{3}{p}=1}$

$\implies\boxed{\mathsf{p=3}}$

$\underline{\textsf{Answer:}}$

$\textsf{The value of p is 3}$

Find more:

The equation whose roots are smaller by 1 than those of 2x2 – 5x + 6 = 0 is 

a) 2x^2– 9x + 13 = 0

b) 2x^2– x + 3 = 0 

c) 2x^2+ 9x + 13 = 0

d) 2x^2 + x + 3 = 0​

https://brainly.in/question/16821146

If x^2-bx/ax-c =m-1/m+1

has roots which are numerically equal but of opposite sign, then the value of'm'must be

(A) a-b/a+b

(B) a+b/a-b

(C) O

(D) 1

soneone please answer this

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