If ?^?– ?? − ? = ? has rational roots then find the minimum value of c, where c is a natural number.
=================================
To Join Online Classes for Quant (Maths) , DI , LR (Reasoning) for CAT / SSC / BAKING – https://www.3elearning.in/
To join off line classroom at Ranchi : visit – https://goo.gl/SaezYz
=================================
Learning Anytime Anywhere.
Free and best youtube learning platform, for CAT/ XAT /SNAP/ CMAT/ SSC / BANKING/ Maths By Amiya
=================================
For more JOIN FB GROUP – https://www.facebook.com/groups/MBAMathsByAmiya/
LIKE – https://www.facebook.com/MathsByAmiya
Telegram Channel : https://t.me/mathsbyamiya
To Join Telegram Group: https://t.me/joinchat/F_j9Dw9Mgi6Je4JSoUd9AQ
Website: www.3elearning.in
Twitter: https://twitter.com/3Eamiya
Best Maths Questions, Best Maths Questions for CAT, CLAT, SSC, UPSC, BANKING, PO, SBI, SNAP, IIFT, XAT, SSC CGL , SAT, GMAT, GRE
source
-6
-49/4
If we had missing terms then?
8
8
C=8
b^2-4ac
7^2-4×1×-c
C=-49/4
-49/4
8 is minimum value of C
8
Minimum value of c is 8. The discriminant 49 + 4c must be = some perfect square = y^2 (say), otherwise the roots won't be rational. So c should be (y^2 – 49)/4, which should be >=1 since c is a natural no. –> y^2 >= 53 –> y^2 =81 gives c as lowest possible natural no. which is 8 (for y^2 = 64, c comes out as 15/4, a fraction).
53/4
C=8 for perfect square
Multinomial formula se kuch or ans aata h sir g.
8
-6
-12
value of c=8, 𝒙^𝟐– 𝟕𝒙 −8 ,solving this we get two rational roots i.e 8,-1..
8 is the answer
Discriminant =D= 49 +4c
As c is natural number, so, D can't be zero.
So, For rational roots, D has to be perfect square
For ,minimum c=8, D = 49+32= 81= 9^2
c=0
C=8,for which under root D=b2-4ac will be perfect square hence give rational roots
8
– 12.25
Minimum value for c = -12
when any middle term is missing then what will be the answer? anyone suppose if X'2 is not here what will be the answer?
C =-49/4
min value of c= 8
8