How do you find if an equation has equal roots?
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How do you find if an equation has equal roots?
– If b2 – 4ac = 0 then the quadratic function has one repeated real root. – If b2 – 4ac < 0 then the quadratic function has no real roots. 1 The equation x2 + 3pq + p = 0, where is a non-zero constant, has equal roots.
What is the discriminant if the roots are equal?
The discriminant (EMBFQ)
| Nature of roots | Discriminant |
|---|---|
| Roots are non-real | Δ<0 |
| Roots are real and equal | Δ=0 |
| Roots are real and unequal: rational roots irrational roots | Δ>0 Δ= squared rational Δ= not squared rational |
What does it mean when an equation has two equal roots?
Hint: A quadratic equation has equal roots iff its discriminant is zero. A quadratic equation has equal roots iff these roots are both equal to the root of the derivative.
Which of the following equation has equal roots?
Answer: Using the standard ax^2 + bx + c =0, the quadratic will have two equal roots if the discriminant b^2 – 4ac = 0.
What are two equal real roots?
If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots. Therefore, there are two real, identical roots to the quadratic equation x2 + 2x + 1. D > 0 means two real, distinct roots.
When discriminant is zero then roots are?
Clearly, the discriminant of the given quadratic equation is zero. Therefore, the roots are real and equal.
When the discriminant is zero then the roots are real numbers and equal?
When a, b and c are real numbers, a ≠ 0 and discriminant is zero (i.e., b2 – 4ac = 0), then the roots α and β of the quadratic equation ax2 + bx + c = 0 are real and equal.
Can zero be a double root?
0 is a root of f(x)=0 and of f′(x)=0 thus it is a double root, with order of multiplicity 2.
What is the sum of the roots of a quadratic equation?
Roots will be equal if and only if Descriminant is equal to 0 i.e b^2 -4ac=0……so in above quadratic equation b can be replaced with (c-a) and a = (b-c) and c= (a-b)….so putting value of a,b,c in above equation we have….. hence proved.. . here, the coefficients add up to 0 which means 1 is a root here. so, sum of roots=2. Hence proved.
How do you prove 2a=b+c?
If the roots of the equation (a-b)x 2 + (b-c)x + (c-a) = 0 are equal , the prove 2a=b+c. Answer. If the quadratic equation ax2 + bx + c has equal roots then its discriminant is equal to zero.
How to find the root of X – alpha (X – Beta)?
Let alpha, beta be the roots of the equation (x – a) (x – b) = c, c≠ 0 . Then the roots of the equation (x – alpha) (x – beta) + c = 0 are Let α,β be the roots of the equation (x −a)(x−b) =c,c = 0. Then the roots of the equation (x−α)(x −β) +c =0 are