Question

WILL MARK BRAINLIEST AND RATE 5 STARS

Answer 1

A) No solutions, because the number under the square root symbol in the quadratic equation (b^2 - 4ac) is negative. 

B) One solutions, because the number under the square root symbol in the quadratic equation (b^2 - 4ac) is equal to 0. 

Answer 2

Answer:  The correct options are

(1) (a) No solutions.

(2) (b) One solution.

Step-by-step explanation:  We are given to find the number of real solutions to the following two quadratic equations:

$-4x^2+7x-8=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x^2+18x+27=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We know that

for quadratic equation $ax^2+bx+c=0~a\neq 0,$ the type of solution depends on the discriminant $D=b^2-4ac$ as follows:

(i) there are two real solutions if  D is greater than 0.

(ii)  there is one real solution if  D is equal to 0.

(ii) there is no real solution if D is less than 0.

For equation (i), we have

a = -4, b = 7  and  c = 8.

Therefore, the discriminant is given by

$D=b^2-4ac=7^2-4\times (-4)(-8)=79-148=-69$

So, there will be no real solution.

For equation (ii), we have

a = 3, b = 18  and  c = 27.

Therefore, the discriminant is given by

$D=b^2-4ac=18^2-4\times 3\times 27=324-324=0.$

So, there will be one real solution.

Thus, the correct options are

(1) (a) No solutions.

(2) (b) One solution.