Question

If the difference of roots of x² - 3px +4 = 0 is 2√5, then the value of p is :
a) ±4
b) +3, -2
c) ±√2
d) None Of These.

#SARWAR CLASSES. AMU ENTRANCE TEST

Answer 1

hey mate !!!

here is your answer !!!

here sum of zeros is = -b/a = 3p /1 => 3p

Product of zeros = c/a = 4/1 = > 4

now we have to

let the first root be x and other be y

now ,

x-y = 2✓5 ----------(1)

or

y-x = 2√5

for convince we take equation ---1

using this formula we get

(x-y)² = (x+y)² - 4xy

(2√5)² = (3p)² - 4 * 4

4*5 = 9p² - 16

20 +16 = 9 p²

36 /9 = p²

p = ±2

hence , Option number " D " is correct .

answer is ±2 that is Option number " D ".

hope it helps:D

thanks

Answer 2

HELLO DEAR,



LET THE ROOTS OF THE EQUATION IS
A and B




given that:-

a=1

b=-3p

c=4

A-B =2√5------------(1)


WE KNOW THAT:-

A+B = -b/a = -(-3p/1) = 3p--------(2)

and,

AB = c/a = 4/1 = 4--------(3)



use this Formula:-

${(a + b)}^{2} - {(a - b)}^{2} = 4ab$
now put the values,

we get,

${(3p)}^{2} - {(2 \sqrt{5} )}^{2} = 4(4) \\ \\ = > 9 {p}^{2} - 20 = 16 \\ \\ = > 9 {p}^{2} = 16 + 20 \\ \\ = > 9 {p}^{2} = 36 \\ \\ = > {p}^{2} = \frac{36}{9} = 4 \\ \\ = > p = + - 2$

hence option (d) none of these is correct


I HOPE ITS HELP YOU DEAR,
THANKS