Answer:
Option 1,3,4,6 are correct
Explanation
Explanation:
we have formula for discriminant that is D=b^{2} -4acD=b
2
−4ac
when D>0 the roots are real and unequal
when D= 0 roots are real and equal
and when D< 0 roots are imaginary or not real and unequal
In 1st equation: x^2+6x+8x
2
+6x+8
a=1,b=6,c=8 on substituting the values in the formula we will get
D=6^2-4(1)(8)=4 > 0D=6
2
−4(1)(8)=4>0 hence real and unequal roots.
In 2nd equation:x^2+4x+8x
2
+4x+8
a=1,b=4,c=8 on substituting values in formula
D=4^2-4(1)(8)=-16 < 0D=4
2
−4(1)(8)=−16<0 so roots are not real
In 3rd equation x^2-12x+3x
2
−12x+3
a=1,b=-12,c=3 on substituting values
D=D=(-12)^2-4(1)(3)=132 > 0D=(−12)
2
−4(1)(3)=132>0 roots are real and unequal
In 4th equation: x^2+4x-1x
2
+4x−1
a=1,b=4,c=-1 on substituting the values
D= 4^2-4(1)(-1)=20 > 0D=4
2
−4(1)(−1)=20>0 real roots
In 5th equation:5x^2+5x+45x
2
+5x+4
a=5,b=5,c=4 on substituting the values
D=5^2-4(5)(4)=-55 < 0D=5
2
−4(5)(4)=−55<0 roots are not real
In 6th Equation: x^2-2x-15x
2
−2x−15
a=1,b=-2,c=-15 on substituting the values
D=(-2)^2-4(1)(-15)=64 > 0D=(−2)
2
−4(1)(−15)=64>0 roots are real