Find the value of ‘p’ for which one root of the quadratic equation Px²-14x+8 =0 is 6 times the other.
Answers
Answered by
24
Heya!
--------
=======================================================
♦Quadratic Equation ♦
========================================================
▪Let the roots be @ and 6@ respectively !
=> We know the relationship between zeroes and Coefficients :
▪Sum of Zeroes = -b/a
=> @ + 6@ = 14/p
=>7@ = 14/ p
=> @ = 2/p.............(1 )
▪Product of Zeroes = c/a
=> @ × 6@ = 8/p
=>6@² = 8/p.............(2)
♦Put @ = 2/p in (2)
=> 6 (2/p)² = 8/p
=>24p = 8p²
=> p = 3
▪Hence the Value of p is 3 .
✔Verification
============
Put p = 3
=> 3x² - 14x + 8 = 0
=> 3x² -2x - 12x + 8 = 0
=> x ( 3x - 2 ) -4 ( 3x - 2 )
=> ( 3x - 2 ) ( x - 4 )
▪Roots are x = 4 , 2/3 ✔
▪Here , 4 is six times of 2/3 .
✔Verified !!.
============
⚪Hence p => 3 ✔✔
===========================================================
--------
=======================================================
♦Quadratic Equation ♦
========================================================
▪Let the roots be @ and 6@ respectively !
=> We know the relationship between zeroes and Coefficients :
▪Sum of Zeroes = -b/a
=> @ + 6@ = 14/p
=>7@ = 14/ p
=> @ = 2/p.............(1 )
▪Product of Zeroes = c/a
=> @ × 6@ = 8/p
=>6@² = 8/p.............(2)
♦Put @ = 2/p in (2)
=> 6 (2/p)² = 8/p
=>24p = 8p²
=> p = 3
▪Hence the Value of p is 3 .
✔Verification
============
Put p = 3
=> 3x² - 14x + 8 = 0
=> 3x² -2x - 12x + 8 = 0
=> x ( 3x - 2 ) -4 ( 3x - 2 )
=> ( 3x - 2 ) ( x - 4 )
▪Roots are x = 4 , 2/3 ✔
▪Here , 4 is six times of 2/3 .
✔Verified !!.
============
⚪Hence p => 3 ✔✔
===========================================================
Similar questions