if alpha and beta are roots of equation 4 x square - 5 x + 2 is equal to zero find the quadratic equation whose roots are alpha +3beta , 3alpha+ beta
Answers
Answered by
21
4x^2-5x+2.let the zeroes be alpha and beta.
sum of zeroes(alpha+beta)=-b/a=-(-5)/4=5/4
product of zeroes(alpha×beta)=c/a=2/4=1/2
let the zeroes of f(x) be 3alpha+betaand 3 beta+alpha
sum of zeroes=3alpha+beta+alpha+3beta
=4alpha+4beta
=4(alpha+beta)
=4×5/4=5
product of zeroes=(alpha+3beta)(3alpha+beta)
=3alpha^2+alpha×beta+9×alpha×beta+3beta^2
3alpha^2+10×alpha×beta+3beta^2
3(alpha^2+beta^2)+10×1/2
3(25/16-1)+5
3(9/16)+5
27/16+5
107/16
f(x)=x^2-(sum of zeroes)x+product of zeroes
=x^2-5x+107/16
=1/16(16x^2-80x+107)
sum of zeroes(alpha+beta)=-b/a=-(-5)/4=5/4
product of zeroes(alpha×beta)=c/a=2/4=1/2
let the zeroes of f(x) be 3alpha+betaand 3 beta+alpha
sum of zeroes=3alpha+beta+alpha+3beta
=4alpha+4beta
=4(alpha+beta)
=4×5/4=5
product of zeroes=(alpha+3beta)(3alpha+beta)
=3alpha^2+alpha×beta+9×alpha×beta+3beta^2
3alpha^2+10×alpha×beta+3beta^2
3(alpha^2+beta^2)+10×1/2
3(25/16-1)+5
3(9/16)+5
27/16+5
107/16
f(x)=x^2-(sum of zeroes)x+product of zeroes
=x^2-5x+107/16
=1/16(16x^2-80x+107)
salonim1:
can you pls explain what did you do after . 3(alpha^2+beta^2) +5
I used a formula i.e., alpha^2+beta^2=(alpha+beta)^2-2×alpha×beta
thx
got it..
Answered by
4
Step-by-step explanation:
Please see the photo
the required quadratic equations is
4x^2-15x +18 =0
Attachments:
Similar questions