ax^2+bx+c=0 has real distinct root if b^2-4ac>0 repeated roots if it =0 and complex roots if ir is <0
For example in your question a=2 b=b and c=3 so for feal distinct roots we want b^2-24>0 b^2>24 so want b<-root24 or b>root24
1) solve the qaudractic eqaution 2x^2 +bx +3=0
2) describe using algebra and words how the nature/ number of roots of the eqaution of Q1 change as b varies, clearly identifying the ranges of the values of b which lead to different types of roots
3) pick a value of b which leads to complex roots and solve 2x^2 + bx +3=0 to confirm this
4) Do the partail fractions questions, it would help me understand if u could do one using the cover up rule, one using substitution method, one using comparing the coeffiecient
a) x-2/((2x+5)(x-6)
b) x^2 -2/((2x+5)(x-6))
c) (x-2)^2/((2x+5)^2(x-6)
d) (x-2)^2/(((2x+5)(x-6)(x+1)))
ax^2+bx+c=0 has real distinct root if b^2-4ac>0 repeated roots if it =0 and complex roots if ir is <0
For example in your question a=2 b=b and c=3 so for feal distinct roots we want b^2-24>0 b^2>24 so want b<-root24 or b>root24